Fixed-time stability of switched systems with application to a problem of formation control

In this paper, a dynamic event‐triggered fixed‐time adaptive fuzzy control method is set up to solve the tracking problem for a type of nonstrict‐feedback switched nonlinear systems with asymmetric tracking error constraints. The proposed method constructs different event‐triggered adaptive fuzzy controllers for different subsystems together with switched update laws and a switching dynamic event‐triggering mechanism (DETM). Under this switching DETM, the difficulty caused by asynchronous switching between candidate controllers of subsystems and subsystems is effectively overcome, and the known limitations on maximum asynchronous time in the existing literature are not needed. Meanwhile, Zeno behavior is avoided by deriving a strictly positive lower bound of interevent times. It is guaranteed that the asymmetric tracking error constraints are never violated and the tracking error can converge to a small neighborhood of origin in a fixed‐time under arbitrary switchings. Finally, the feasibility of the derived theoretical results is demonstrated by employing a numerical example and a switched Chua's Circuit system.

Section: Resultsmentioning

confidence: 97%

Section: Resultsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic event‐triggered fixed‐time adaptive fuzzy control of nonstrict‐feedback switched nonlinear systems

Wang

Long

2022

“…Meanwhile, as proved in Reference 10, the negative definiteness of the Lyapunov function derivative is not a necessary condition for the stability study of switched systems. Many existing works 7,[11][12][13][14] established multiple Lyapunov functions methods to guarantee the asymptotic stability which are more applicable. In the multiple Lyapunov functions methods, a commonly used condition is that the first derivative of the Lyapunov function for each activated subsystem is required to be negative definite.…”

Section: Introductionmentioning

confidence: 99%

Higher‐order derivatives of generalized Lyapunov‐like functions for switched nonlinear systems

Liu

2022

This paper is concerned with utilizing higher-order derivatives of generalized Lyapunov-like functions to infer asymptotic stability of the switched nonlinear system without requiring the first derivative of the Lyapunov function for each activated subsystem to be negative definite. In contrast to the existing switched systems literature, we allow generalized Lyapunov-like functions to increase both during the continuous flows and the discrete jumps. Firstly, a set of sufficient conditions for asymptotic stability of switched nonlinear systems are derived under a state-dependent switching law. Then, all the above-mentioned conditions are transformed to a set of bilinearly diagonally dominant sum of squares constraints. Bilinearly diagonally dominant sum of squares programming is proposed as a tool to solve the conditions provided. Finally, two examples are introduced to prove the effectiveness of the above method.

Further results on fixed‐time stability of time‐varying hybrid systems

Chen,

Yang

2024

The introduction of time‐varying factors makes it difficult and complex to study the stability of hybrid systems. How to improve the traditional stability analysis method to study the stability of time‐varying hybrid systems is a great challenge. In this paper, the fixed‐time stability (FxTS) of time‐varying hybrid systems is investigated. Starting with time‐varying nonlinear systems, two relaxed stability conditions are proposed to verify the FxTS of systems by using the time‐varying Lyapunov functions. Then, the obtained results are extended to study the FxTS of time‐varying hybrid systems, some improved stability conditions are given by combining the methods of minimum dwell time and multiple time‐varying Lyapunov functions. Compared with the existing results, the obtained conditions are less conservative and provide the more accurate estimations for the convergence time of systems. Two numerical examples are given to illustrate the theoretical results.