Finite‐time boundedness of switched systems with time‐varying delays via sampled‐data control

Abstract

In the framework of sampled-data control, finite-time boundedness (FTB) of switched systems with time-varying delays is investigated. Sufficient conditions for FTB of switched systems with time-varying delays via sampled-data control are proposed. Moreover, considering the relationship between the sampling period and the mode-dependent average dwell time, switching signals are designed. In addition, finite-time weighted L 2 -gain (FTW-L 2 -gain) of switched systems with time-varying delays is proposed to measure their disturbance tolerance capacity within a finite-time interval. Multiple Lyapunov-Krasovskii functionals are applied to complete subsequent proofs in detail. Simulation results are exemplified to verify the proposed method. K E Y W O R D S finite-time boundedness, multiple Lyapunov-Krasovskii functionals, sampled-data control, switched systems1 Int J Robust Nonlinear Control. 2020;30:2953-2976. wileyonlinelibrary.com/journal/rnc © 2020 John Wiley & Sons, Ltd. 2953 2954 LIN et al.dynamics, time-varying delays, and exogenous disturbances in switched systems, research on FTB of switched systems with time-varying delays is not a trivial work. With the development of digital technologies and computers, sampled-data controllers are widely used in practice because of advantages of not resulting in degradation of the closed-loop performance and saving the data transmission amount. 21 Based on previous researches, FTB of switched systems with time-varying delays from sampled-data control perspective is to be further investigated to meet the requirements of practical applications. To make resultant closed-loop systems FTB, corresponding controller is usually designed to match with each subsystem. However, when sampled-data controllers are used for switched systems, the active switched subsystem and the matched sampled-data controller may produce mismatched, resulting in inconsistency between the plant mode and the controller mode. 22 This kind of mode mismatching, which is an important subject in the research field of switched systems, 23-27 will produce complex state trajectories and increase complexity of FTB analysis. Therefore, in this note, to implement FTB of switched system with time-varying delays via sampled-data control, it is necessary to conduct in-depth study on the issue about asynchronous switching caused by sampled-data control.It is well known that switching signals have an important impact on FTB of switched systems. [28][29][30] At present, average dwell time (ADT) method is mostly used in the researches of switched systems. [31][32][33][34] The minimum of admissible ADT is determined by two parameters unrelated to the mode. 35,36 In ADT method, switching signals occur during the running time of subsystems, and the design of common parameters is conservative to some extent. The mode-dependent ADT (MDADT) method discussed in References 37 and 38-40 combines switching conditions with certain control gains related constraints to avoid the conservatism of the ADT method. Therefore, in this articl...

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