The existence of time delay may destroy the system performance and even lead to instability.
2. Time delays are often encountered in many fields of science and engineering, and they are usually the source of system performance degradation or instability.
Time delay frequently appears in many fields of science and engineering, and it is usually the cause of system performance degradation or instability.
3. In delay control and delay measurement, delay is usually considered as undesirable, because it tends to worsen the system performance and even make the system unstable.
In the control and measurement with time delay, the time delay is invisible, because it often deteriorates the system performance and even makes the system unstable.
4. Due to the emergence of new applicable theoretical tools and practical problems in the engineering field and formation technology, the research activities on time delay and/or sampling data system analysis and control have been increasing in the past decade (see Sipahi, Niculescu, Abdallah, Michiels and Gu (20 1 1) and Zhang, Branicky and Phillips (200).
In the past ten years, due to the emergence of new adaptive theoretical tools and practical problems in the field of engineering and information technology, the research activities on the analysis and control of time delay and/or sampled data systems have been increasing (see Sipahi, Niculescu, Abdallah, Michiels, Gu(20 1 1) and Zhang, Branicky and Phillips (20).
Recently, people have become more and more interested in the stability of systems with time-varying delays, which has a strong engineering background? Eld, such as network control system, see? For example.
In recent years, the stability of time-delay systems has attracted wide attention, and it has a strong background in engineering fields, such as networked control systems.
6. The time-delay correlation criterion based on LKF method is usually expressed in the form of linear matrix inequality, and its conservatism is usually judged by the upper bound of time-varying delay.
1. Lyapunov-krassovsky function (LKF) method is one of the most popular methods. In LKF, some useful terms are not ignored but considered, which makes the results less conservative.
LF functional method is an important method. Considering some neglected items can reduce conservatism.
1. delay will cause system oscillation or performance degradation. This makes it necessary to study the stability of time-delay systems. In addition to stability, for some applications, it may be crucial to determine the convergence rate or instantaneous decay rate of the system state.
Time lag will lead to system performance degradation. It is necessary to study time-delay systems. In addition to stability, for some applications, it may be very important to determine the convergence rate or instantaneous decay rate of the system state.
1. The idea of cross-coupling control is widely used to design synchronization. Controller? Which one? Is it okay? Is it? Have you seen it? In literary works.
The idea of cross control has been widely used to design synchronous controllers, such as references [2-8].
2. Rolling mill control? Is an example of measuring delay, which can be found in Sbarbaro-Hofer [240]].
Rolling mill control is an example of measuring delay, which can be found in Barbara Hofer [240].
3.？ Analysis of delay resonator? And? Its application? Be reported. In [216,217,63, 125].
[216,217,63, 125] delay resonator and its application analysis.
4.？ For example, a finite-dimensional system can represent a dynamic controller of a system modeled by PDE (see D 'André a Novell, Boustany, Conrad and Rao (1994), krstic (2009) and references therein).
For example, a finite-dimensional system can represent a dynamic controller of a system modeled by PDE (see D 'André a Novell, Boustany, Conrad and Rao( 1994), krstic (2009) and their references).
5. On the contrary, an ordinary differential equation (ODEs) system can simulate a component coupled to the phenomenon described by PDEs in Daafouz, Tucsnak and Valein (20 14).
? On the contrary, as described by Daafouz, Tucsnak and Valein(20 14), ordinary differential equations (ODE) can model the components coupled with the phenomena described by PDE.
6. In the past decades, the robust stability of uncertain systems with time-varying delays has been studied by LKF method, and fruitful results have been achieved.
In the past decades, the robust stability of uncertain time-delay systems has achieved fruitful research results. By using the LKF method,
7. The core idea behind the event-triggered control is that the update of control commands is only executed after the event, rather than periodically passing by with time.
Note: The introduction of specific existing research work is not a simple pile-up, but requires hierarchy, logic and purpose. In a word, it is necessary to highlight the necessity and importance of research through the existing achievements. Basically, it can adopt a general-sub-general structure,
General: the main direction, ideas and methods of research.
Points: according to different directions, list references; Be careful not to list at will, be representative, and comment on the article, pointing out shortcomings or advantages. Is the purpose of this part still to highlight? The superiority of one's own article.
Summary: To sum up, the purpose of this study is to solve the shortcomings in the existing literature.
1. The time domain method based on Lyapunov stability theory has been widely used. Among some stability conditions based on inequality, linear matrix inequality (LMI) method has become an effective and popular method to solve the stability problem of power system. Time-varying delay (see [4], [6] and [9]-[ 12]).
The time domain method based on Lyapunov stability theory has been widely studied. In the stability condition based on inequality, linear matrix inequality method is an effective tool to solve the stability problem of time-varying delay power system.
2. In order to deal with time-varying and random delays, an indirect time-domain method based on Lyapunov stability theory and linear matrix inequality (LMIs) is proposed as an effective method to obtain approximate delay margin [13].
In order to deal with time-varying delay and random delay, the time-domain direct method based on Lyapunov stability theory and linear matrix inequality technology has become an effective method to obtain the approximate value of delay margin.
3. In order to reduce the conservatism of the stability conditions of time-varying time-delay systems, many methods have been proposed. The main work focuses on two aspects: first, the techniques of constructing L-K functionals, such as delayed division functionals, time-dependent functionals of matrices [13], functionals containing triple integral terms [14], and quadratic functionals multiplied by higher scalar functions [15]. The other is the analysis method to estimate the derivative of L-K functional with respect to time, such as the improved optimization technique, the free weight matrix method [16], and the integral inequalities include Jensen inequality [1 1], Wirtinger inequality [17], and the integral inequality based on auxiliary functions [/kloc-6]. And then what? Combining the convex combination idea of linear convex analysis [19], reciprocal convex technique [20] and quadratic convex method [2 1].
Many methods are used to reduce the conservatism of stability criteria for time-varying time-delay systems. The main work focuses on two aspects: one is the construction of L-K functional, such as: partition function with time delay, whose function matrix depends on time delay [13], function with triple integral term [14], and quadratic term multiplied by higher-order scalar function [15]. On the other hand, it is an analysis method to estimate the time derivative of L-K functional, such as improved specialization technique, free weighted matrix method [16], Jensen inequality [1 1], Wirtinger inequality [17], and integral inequality based on auxiliary function [/kloc].
4. In the past ten years, there have been a lot of researches devoted to the construction of Lyapunov-krassovsky functional, aiming at reducing the inherent conservatism of this method.
In the past 10 years, a lot of research has been devoted to constructing L-K functionals, aiming at reducing the inherent conservatism.
4. 1? In addition to the choice of functional, an important source of conservatism also depends on the constraint mode of cross terms when dealing with Lyapunov-krassovsky functional derivatives.
In addition to the choice of functional, another source of conservatism is the cross term generated when dealing with the derivative of L-K functional.
1. Zhang et al. [1] developed several chaotic speed synchronization controllers for induction motors by using stators? Ux regulations.
A chaotic speed synchronization controller for multiple induction motors is developed by using stator flux adjustment technology.
2. Starting from the semigroup modeling of partial differential equations, the authors of Gahrawat and Li Dingding (20 17) constructed a very general Lyapunov functional, and its parameters were optimized by the sum of squares process (see Ahmadi, Valmorbida, & ampPapachristodoulou, 20 16).
In (20 17), the author constructs a very generalized Lyapunov functional from the semigroup model of partial differential equations, and its parameters are optimized by the sum of squares process.
1. Combined with the simple choice of Lyapunov-krassovsky functional, this inequality leads to a new stability criterion for linear time-delay and sampled data systems.
? Combined with simple Lyapunov-krassovsky function, this inequality can obtain new stability criteria for linear time-delay and sampled data systems.
1. In the existing literature? Literature report
2. In the past ten years?
3. Has the research result been popularized? This research result can be extended to other fields.
4.？ The purpose of this article is to discuss? The purpose of this paper is to discuss (present, describe)
5. Do you understand? Complete, acquire, acquire, produce, reach, produce, acquire and realize.
6. The results show that? This result (fact, argument, explanation, classification, comparison, analysis) gives (shows)?
7. This formula is based on? These formulas are derived from?
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