Document Positioning

This document's task is not to continue supplementing knowledge content, but to transform the understanding already organized in previous sections into directly expressible output templates. These are intended for use in thesis defenses, job interviews, presentations to advisors, descriptions of research directions in resumes, and oral presentations of paper reading reports.

If the previous documents addressed "Do I truly understand these papers?", then this one addresses another equally critical matter:

Can I articulate my understanding professionally, accurately, and clearly in different scenarios?

Therefore, this section emphasizes not memorizing more knowledge points, but transforming existing content into stable, reusable expression units. You can think of it as an "output toolbox."

Quick Introduction Template for the Overall Research Direction

During a defense or interview, professors usually don't start by asking for details. Often, they first ask something like, "What is your overall research direction?" At this moment, the most important thing is not to talk a lot, but to speak accurately, first clarifying the research object, research context, and the division of focus between the two papers.

30-Second Version

Overall, these two papers belong to research on the stability of complex large-scale stochastic systems under network attacks. They share a common focus on the problem of whether a system's state can maintain exponential stability when the system simultaneously has node coupling, stochastic disturbances, and asynchronous behavior, and when the control links are affected by DoS attacks. Specifically, one paper focuses on achieving stability through decentralized control with discrete observations under switching and time-delay conditions; the other focuses on establishing a unified stability analysis framework under the combined effects of asynchronous impulses and DoS attacks.

1-Minute Version

Both papers revolve around research on the stability of complex large-scale stochastic systems under asynchronous DoS attacks. The common problem is that when a system has node coupling, stochastic disturbances, and asynchronous behavior, the ideal assumptions of traditional synchronous, continuous communication, and continuous observation no longer hold. Therefore, it is necessary to study whether the system can remain stable under attack and resource-constrained conditions. The first paper studies large-scale stochastic systems with switching and time-varying delays, focusing on how to design a controller to achieve mean-square exponential stability under the conditions of only discrete observations and the use of decentralized control. The second paper studies large-scale stochastic networks with asynchronous impulse effects, focusing on how to establish a unified stability analysis framework under the combined effects of stabilizing impulses, destabilizing impulses, continuous feedback control, and DoS attacks. Overall, one leans more towards control design, and the other leans more towards unified analysis, but both serve the common direction of stabilizing complex systems in asynchronous network attack environments.

3-Minute Version

My research direction across these two papers can be summarized as the stability analysis and stabilization control of complex large-scale stochastic systems in asynchronous network attack environments. The common problem both papers address is whether a system's state can maintain exponential stability when the system is composed of multiple nodes with coupling between them, is affected by stochastic disturbances, and, additionally, suffers from unreliable control links due to DoS attacks. The first paper studies large-scale stochastic systems with switching and time-varying delays. It considers practical factors such as node-dependent switching, discrete observations, decentralized control, and mismatches between controller modes and system modes. The focus is on designing a control law based on locally sampled states and proving that the system can still achieve mean-square exponential stability. The second paper studies large-scale stochastic networks with asynchronous impulse effects. It considers not only continuous feedback control but also the application of impulse corrections to the system state at certain discrete moments. It further unifies the treatment of stabilizing impulses, destabilizing impulses, attack intervals, and non-attack intervals to provide a unified exponential stability criterion. Methodologically, both papers use Lyapunov methods, balancing functions, and graph theory tools. The difference lies in that the first paper leans more towards control design in complex scenarios, while the second leans more towards unified stability analysis in asynchronous hybrid systems.

Concise Introduction Template for a Single Paper

After the professor knows you have worked on two papers, the next common question is, "Then, tell me what each paper is about." The biggest risk here is diving straight into symbolic details, causing the main thread to be lost. A better approach is to first use a paragraph to clearly explain the object, mechanism, and contribution of each paper.

Introduction Template for the First Paper

The first paper primarily studies how to achieve stability for large-scale stochastic systems with switching and time-varying delays under asynchronous DoS attacks through decentralized control with discrete observations. Its characteristic is that the controller does not rely on continuous observation but only acquires local states at sampling moments and applies negative feedback control based on the most recently sampled mode and state. Simultaneously, the paper considers practical factors such as node-dependent switching and mode mismatch. Ultimately, it proves that the system can achieve mean-square exponential stability through Lyapunov functionals, balancing functions, and graph theory methods.

Introduction Template for the Second Paper

The second paper primarily studies how to achieve stability for large-scale stochastic networks with impulse effects under asynchronous DoS attacks. Its characteristic is that the system evolves not only in continuous time but also undergoes impulse jumps at certain discrete moments, and these impulses can either be stabilizing or destabilizing. The core contribution of the paper is to unify stabilizing impulses, destabilizing impulses, attack intervals, and non-attack intervals into a single stability analysis framework using balancing functions and Lyapunov methods, ultimately providing a mean-square exponential stability criterion.

Answer Template for Similarities and Differences Between the Two Papers

"What are the similarities and differences between these two papers?" is almost a guaranteed question. The most common mistake when answering this is to only use abstract terms, such as "both study stability" or "one leans towards control, the other towards analysis." While the direction of such answers is not wrong, they are too vague. A better approach is to place the commonalities in the research object, problem background, and methodology, and the differences in the stabilization mechanisms and paper focus.

Concise Version

The commonality between the two papers is that they both study the stability problem of complex large-scale stochastic systems under asynchronous DoS attacks. Both consider stochastic disturbances, node coupling, and asynchronous behavior, and both employ Lyapunov methods, balancing functions, and graph theory tools. The differences lie in that the first paper leans more towards control design in complex scenarios, focusing on how to achieve stability through decentralized control with discrete observations; the second paper leans more towards unified stability analysis, focusing on how to establish a unified criterion under the combined effects of asynchronous impulses and DoS attacks.

Slightly Expanded Version

The main research thread of the two papers is consistent: both study how complex large-scale stochastic systems maintain exponential stability in network attack environments. The commonalities are that the research objects both have node coupling and stochastic disturbances, and both emphasize that asynchrony is more realistic than traditional synchronous models. The differences are mainly reflected in the mechanisms and focus. The system model in the first paper is more complex, containing switching, delays, discrete observations, and mode mismatch, with the focus on designing an implementable decentralized controller. The second paper focuses on impulse effects, especially on how to establish a unified stability analysis framework under asynchronous attacks when stabilizing and destabilizing impulses coexist.

How to Answer "How does the first paper achieve stability? How does the second?"

This question seems simple but actually tests whether you have truly grasped the differences in the stabilization mechanisms between the two papers. When answering, don't just say "the first relies on control, the second on impulses"—that's too coarse. Clearly state how the control in the first paper enters the system and why the stabilization mechanism in the second is more like a hybrid mechanism.

You can answer directly like this:

The first paper primarily achieves stability through feedback control with discrete observations. Its control law, based on the node's most recently sampled local state and mode, continuously applies negative feedback to pull the system state back towards the equilibrium point. The second paper does not rely solely on continuous control but achieves stability through the combined action of continuous feedback control and impulse interventions. That is, in the second paper, the system's state growth is continuously suppressed by negative feedback control during non-attack intervals, while at certain discrete moments, the state is instantaneously corrected through impulse mappings. Therefore, it resembles a hybrid stabilization mechanism where continuous control and discrete intervention work together.

How to Answer "What is an impulse, and why is an impulse also considered a human intervention?"

This is a common follow-up question for the second paper. Because many listeners encountering impulse systems for the first time might interpret an impulse as "the system jumps on its own." Here, it's crucial to articulate that "an impulse is a state intervention at discrete moments."

You can say it directly like this:

An impulse refers to an instantaneous jump or instantaneous correction of the system state at certain discrete moments. Although it is not written in the traditional form of a control input, it essentially represents an external mapping directly applied to the system state at those moments, thus also considered a form of human intervention. Compared to continuous feedback control, impulse control does not apply action continuously but performs instantaneous corrections to the state at several critical moments.

If the other party continues to inquire, you can add:

The first paper is more like continuously adjusting the input in daily operation, while the second allows directly modifying the state at certain moments.

How to Answer "What is unified stability analysis?"

"Unified stability analysis" is a keyword in the second paper, but merely repeating these words mechanically is usually insufficient to convince. When answering, it's best to divide it into two levels: "definition" and "significance."

Concise Version

Unified stability analysis means not having to separate and prove many different cases individually, but using a common theoretical framework to incorporate them all into the same stability criterion for analysis.

Expanded Version for the Second Paper

In the second paper, unified stability analysis mainly refers to no longer discussing stabilizing impulses, destabilizing impulses, attack intervals, and non-attack intervals separately. Instead, by constructing balancing functions and Lyapunov functions, these different factors are unified into a single stability criterion to determine whether the system can still achieve exponential stability in an asynchronous hybrid environment.

Further Explanation of Its Significance

The role of this approach is to make the theory more general and closer to reality, while avoiding a large amount of fragmented case-by-case discussion. It also makes it easier to see which mechanisms the system relies on to achieve stability.

How to Answer "If the system is unstable, what exactly is unstable?"

This question is well-suited to demonstrate whether you have grounded "stability" in specific state variables. Don't answer with vague statements like "stability becomes worse." Clearly point out that what is being stabilized is the system state.

You can say it directly like this:

In the papers, so-called system instability essentially means the system state cannot converge to the equilibrium point. In the first paper, what is unstable is the overall state $\rho(t)$; in the second paper, what is unstable is the overall state $\eta(t)$. Control does not abstractly control "stability" but acts on the system equations to change the evolution trend of these states, causing them to eventually converge to zero.

How to Answer "Why is control also needed during normal times?"

Behind this question often lies a misunderstanding that stability issues only arise when DoS attacks occur. In your answer, clarify that "the system itself is not necessarily inherently stable."

You can say it like this:

Because the systems in these two papers are not necessarily inherently stable. Even without DoS attacks, the systems already contain factors like node coupling, stochastic disturbances, delays, switching, or impulses that could cause instability. Therefore, feedback control or impulse intervention is needed during normal times to suppress state growth. DoS attacks are not the sole destabilizing factor; they further weaken the control effect on an already complex system.

How to Answer "Why do certain terms make the Lyapunov derivative positive, while the control term can push it back to negative?"

This question often appears when professors probe the depth of methodological understanding. Use the language of "energy change" in your answer to appear more solid.

You can say it like this:

The Lyapunov function essentially represents an energy function for the magnitude of the system state. If certain terms cause the state to continue moving away from the equilibrium point, they typically manifest as positive growth terms in the Lyapunov derivative. If the control term has a negative feedback structure, it provides a negative dissipation term in the derivative. The key to the stability proof is to design the control such that these negative terms are sufficiently large to overcome the positive growth terms brought by the system's own dynamics, coupling, noise, or destabilizing impulses, thereby keeping the total derivative trending negative.

How to Answer "Why can we still analyze when $F$'s specific form is unknown?"

This is a typical methodological follow-up question. You cannot answer with "because it can be approximated"—that's not accurate enough. Emphasize that "the analysis relies on growth bounds, not on precise analytical forms."

You can say it like this:

Stability analysis typically does not require knowing the precise analytical form of $F$, but only requires that it satisfies some growth bound or Lipschitz condition. That is, we don't need to know exactly what it looks like, only the maximum extent to which it can grow. This allows us to transform the unknown function into upper-bound terms involving the state magnitude in the Lyapunov estimation, enabling the stability analysis to proceed.

Research Direction Descriptions Suitable for Resumes or Self-Introductions

Descriptions in a resume cannot be too long or too abstract. It's best if they can reflect both the research context and your methodological characteristics.

Concise Version

Research direction: Stability analysis and stabilization control of complex large-scale stochastic systems in asynchronous network attack environments.

Slightly Expanded Version

Primarily studies stability problems of large-scale stochastic systems under asynchronous DoS attacks, focusing on methods such as decentralized control with discrete observations, impulse intervention, and unified stability analysis.

Interview-Oriented Version

My research mainly revolves around the stabilization of complex stochastic network systems under network attacks. One part of the work focuses on control design under conditions of discrete observation and decentralized control, while another part focuses on unified stability analysis in asynchronous impulse systems.

Questions Professors Might Ask and Answering Directions

During defenses and interviews, many questions are not part of your prepared main content but are follow-ups from professors based on what you said. Without prior preparation, it's easy to panic. The following follow-up questions are very typical.

Why is the first paper more focused on control design than the second?

Answering direction can be captured like this: The first paper explicitly designs a decentralized control law with discrete observations, focusing on controller structure and implementation mechanisms. The second paper, although it also has control terms, has its main focus more on impulse effects and the unified analysis framework. Therefore, the paper's emphasis is not on controller structure innovation but on the unification of stability analysis.

Why can't the second paper simply be viewed as an ordinary control paper?

Answering direction can be captured like this: The second paper is not just about designing control inputs; it also handles impulse mappings, the coexistence of stabilizing and destabilizing impulses, asynchronous attack intervals, and asynchronous node behavior. What it truly aims to solve is how to establish a unified stability criterion in complex hybrid scenarios, making it more inclined towards a theoretical analysis framework.

What is the role of the balancing function?

Answering direction can be captured like this: It is a time-dependent weighting function used to uniformly record the total influence of stabilizing and destabilizing factors across different intervals. In the first paper, it balances attack intervals, mode mismatch, and asynchronous switching; in the second paper, it balances impulse types, attack intervals, and asynchronous impulse behavior.

Why not just use an ordinary Lyapunov function?

Answering direction can be captured like this: Because the system has complex structures like delays, impulses, attack intervals, and asynchronous behavior, a simple $|x|^2$ cannot fully absorb these influences. Therefore, more complex Lyapunov functionals and time-varying weighting structures are needed.

What is the common methodology of the two papers?

Answering direction can be captured like this: Both first construct node-level Lyapunov functions or functionals, then introduce balancing functions to handle asynchrony and interval differences, use graph theory to handle coupling terms, and finally derive the mean-square exponential stability criterion for the overall system.

Vague Statements Easily Made During Defenses and How to Make Them More Precise

Many expressions seem fine in one's mind but sound too general when spoken aloud. The following are examples of statements that are "correct but not good enough" and often appear in defenses.

Vague Statement 1

"Both papers study stability problems."

Better way to say it:

Both papers study the mean-square exponential stability problem of complex large-scale stochastic systems under asynchronous DoS attacks.

Vague Statement 2

"The first is about control, the second is about analysis."

Better way to say it:

The first leans more towards stabilization design under decentralized control with discrete observations, while the second leans more towards unified stability analysis under the combined effects of asynchronous impulses and DoS attacks.

Vague Statement 3

"The second achieves stability through impulses."

Better way to say it:

The second achieves stability through the combined action of continuous feedback control and impulse intervention, where stabilizing impulses provide instantaneous contraction effects, while DoS attacks weaken the continuous control effectiveness.

Vague Statement 4

"The Lyapunov method proves stability."

Better way to say it:

By constructing Lyapunov functions or functionals, the paper unifies system dynamics, control terms, attack effects, and impulse effects into a rate-of-change inequality, ultimately proving that the overall decay outweighs the overall growth, thereby obtaining the mean-square exponential stability conclusion.

The core principle behind these revisions is simple: Speak less of abstract conclusions and more about the logical relationships between the research object, mechanisms, and conclusions.

A Suitable Paragraph for Concluding Summary

Before the end of a defense or presentation, a sentence to tie everything together is usually needed. At this point, do not introduce new information points; instead, tighten the main research thread again.

You can directly use the following paragraph:

Overall, these two papers both revolve around research on stabilizing complex large-scale stochastic systems in asynchronous network attack environments. The first paper focuses on designing