Stability of switched systems with limiting average dwell time

Summary Based on proportional‐integral‐derivative (PID)/PD controls, we in the article investigate the tracking problem of a class of second‐order time‐varying switched nonlinear systems. To start with, for tracking a given point under arbitrary switching signals, we propose a sufficient condition about PID controller parameters, which can be implicitly described as semialgebraic sets. Successively, we consider the tracking problem under average dwell time (ADT)‐based switching signals and propose an alternative sufficient condition about PID controller parameters. Especially, for tracking an equilibrium point of the system without controls, we can further simply utilize the proportional‐derivative control and similarly construct corresponding semialgebraic conditions about proportional‐derivative controller parameters under arbitrary switching signals and ADT‐based switching signals. Finally, two examples are given to show the applicability of our theoretical results.

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Section: Pid Controlled Time-varying Switched Systemsmentioning

confidence: 99%

Design proportional‐integral‐derivative/proportional‐derivative controls for second‐order time‐varying switched nonlinear systems

She

Zhang

et al. 2019

Intl J Robust & Nonlinear

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“…The main reason is from the frequency change, switching phenomenon, or some sudden noise interference, we call these phenomena impulsive effects. [29][30][31][32] They existed widely in various biological networks described by impulsive differential systems, which are always showed in the nodes for many NNs. In natural science and technology, they are successfully used to model many practical problems.…”

Section: Introductionmentioning

confidence: 99%

A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses

Lou

et al. 2020

Intl J Robust & Nonlinear

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In this article, the stability of quaternion-valued neural networks (QVNNs) with hybrid impulses is investigated, which contain stabilizing impulses and destabilizing impulses simultaneously. Through constructing the relationship between impulses and quaternions, this article has obtained a unified criterion for the global exponential stability of the system. First, a new form of impulsive representation is constructed, and the established systems can be decomposed into four different real parts. According to the characteristics of the impulses, the system divides the average interval of impulses (AII) into two cases, that is, T < ∞ and T = ∞, which can process hybrid impulses simultaneously. Second, for QVNNs, by using the method of matrix p-norm and the inequality technology, the criterion of each interval is derived. Considering the impulsive effects on the overall stability of QVNNs, the uniform criterion for the global exponential stability can be obtained. In addition, the convergence rate of QVNNs with hybrid impulses is also discussed. Finally, in order to verify the theoretical conclusions, some numerical simulations are given.

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“…For instance, a switched system which is composed of all unstable subsystems may lead to the stability of the closed-loop system provided that the switching law is properly designed. [11][12][13][14][15][16][17] In the past few decades, the common Lyapunov function 18 has been applied to the systems under arbitrary switching. Compared with common Lyapunov function, the multiple Lyapunov function (MLF) 4 is more flexible under restricted switching, which overcomes the difficulty of finding a common Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

Reachable set estimation and synthesis of discrete‐time switched systems

Zhao

Wang

Zuo

2020

Intl J Robust & Nonlinear

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This article focuses on estimating the reachable set of discrete-time switched linear systems with unknown disturbance. The discontinuous multiple Lyapunov function, which enables us to reduce the conservatism in the sense of mode-dependent average dwell-time, is proposed to estimate the underlying reachable set. The main difficulty of this problem is that the energy may jump at the switching instants. To this end, we seek for another set, which preserves the former reachable set as an inner one, guaranteeing that in the case of escaping the inner reachable set at the switching instants, the state trajectory will arrive at the inner reachable set within finite time. Finally, two numerical examples are given to show the efficiency of the proposed strategy.

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Stability of switched systems with limiting average dwell time

Cited by 26 publications

References 48 publications

Design proportional‐integral‐derivative/proportional‐derivative controls for second‐order time‐varying switched nonlinear systems

Design proportional‐integral‐derivative/proportional‐derivative controls for second‐order time‐varying switched nonlinear systems

A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses

Reachable set estimation and synthesis of discrete‐time switched systems

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