Quasi‐time‐dependent asynchronous filtering for discrete time switched systems via the event triggering mechanism

Abstract

This article is concerned with the quasi-time-dependent asynchronous  ∞ filter design problem for a class of discrete-time switched systems via the event-triggering mechanism. Applying the quasi-time-dependent Lyapunov functions and the mode-dependent average dwell time technique, an asynchronous  ∞ filter is designed with a weighted performance index; the filter parameter matrices are quasi-time-dependent in each event-triggering-dependent sampling interval; both cases (Case 1: no more than one switching, Case 2: multiple switchings) are taken into account in this sampling interval, by which the assumption, that the maximal asynchronous period is not larger than the minimal dwell time, is relaxed in this article. Simulation examples are given to show the less conservatism and effectiveness of the proposed results. K E Y W O R D S event triggering mechanism, mode-dependent average dwell time, quasi-time-dependent asynchronous filter 1 INTRODUCTION Switched systems have attracted much attention due to their powerful applications in modeling some physical systems such as mobile robots, 1 the flight control systems, 2 and so on. Switched systems consist of subsystems and a switching law by which these subsystems are activated in some time intervals. For switched systems, 3-12 the switching law has an important role in the performance analysis and synthesis, which results in that several classes of switching laws appear, such as Markov-dependent switching laws, 6,11,13 and dwell time-dependent switching laws. 3-5,7-10,12 By the former switching law, switchings among subsystems take place dependent on the transition probability; while, by the later switching law, switchings among these subsystems depend on the dwell time conditions. For switched systems with dwell time-dependent switching laws, the average dwell time (ADT) technique 3,4,8,9,14 and the mode-dependent average dwell time (MDADT) technique 12,15,16 are commonly used to study the stability analysis and controller design. In contrast with the former, much freedom can be provided to the conditions by the latter because each subsystem has its own ADT. On the other hand, since the system state may be immeasurable, much attention was paid to the study of the state estimation 17,18 and filter, such as the reliable filter, 19 dissipativity-based filter, 20 generalized  2 filter, 21 and so on. By applying measurable output vectors, the filter and state estimation were designed to guarantee that the estimation error satisfies some performances. 13,22-28 In particular, the  ∞ filter or  ∞ control has attracted much attention, 25,27-34 because the external disturbances are not required to satisfy some statistic constraints. However, in References 22,27-32, the data

Reliable extended dissipative control for switched systems based on event‐triggered communication scheme

“…Thus, under the proposed event-triggered transmission (5), the mismatch relationship between the subsystem and its corresponding controller is raised, that is to say, there will be an asynchronous switching between the subsystem and the corresponding controller. Inspired by Zhao et al 10 and Xiao et al, 32 let…”

“…Over the past few decades, a great number of important progress and remarkable achievements have been made on issues about stability analysis and control synthesis problems of switched systems. [6][7][8][9][10] The multiple Lyapunov-Krasovskii functional (MLKF) technique and average dwell time (ADT) method are effective as a basic tool to obtain a prescribed performance of switched systems. In addition, the failure of control components is unavoidable due to harsh environmental factors and potential process abnormalities; thus, the actuator cannot provide a reliable information and data.…”

Extended dissipative-based state estimation for Markov jump coupled neural networks with reaction-diffusion terms

“…In order to model such NNs, the Markov jump parameters is introduced (Dai et al, 2019; Selvaraj et al, 2018; Song et al, 2019b; Xu R et al, 2017). In the past few years, researchers have also made some results on MJNNs, including stability analysis (Jiao et al, 2018; Samidurai et al, 2016; Xu and Sun, 2019), synchronization control (Cheng et al, 2017; Song et al, 2020; Xu Y et al, 2017), and asynchronous filtering (Shen et al, 2018; Zhao et al, 2020; Zhou et al, 2020). However, the extended dissipation analysis of Markov jump coupled NNs (MJCNNs) is rarely considered.…”