Dwell‐time‐based control synthesis of switched positive systems with all unstabilizable subsystems

Abstract

This article investigates the robust exponential stabilization of a class of switched positive systems with uncertainties by co-designing controllers for subsystems and dwell time switching strategy. The uncertainties refer to interval uncertainties. One of the distinguishing features is that none of the forced individual subsystems is assumed to be stabilized. The other feature is that the stabilization for the unforced switched system can not be solvable by designing dwell time switching signal. First, for switched positive systems without uncertainties, a type of multiple time-varying co-positive Lyapunov functions is used, and the computable sufficient conditions on the state feedback controller for each subsystem are derived in the framework of dwell time strategy. Moreover, the exponential stabilization problem is solved by confining the lower and upper bounds of the dwell time, restricting the upper bound of derivative of considered Lyapunov function of the active subsystem, and decreasing the Lyapunov function values at successive switching instants of the overall switched system.Then, the results are extended to the robust exponential stabilization case for switched positive systems with uncertainties, and sufficient conditions are given in the same framework of the dwell time for that of the forced switched systems by further designing state feedback controllers. Finally, illustration examples are given to illustrate the effectiveness of the proposed methods.

A Switching Strategy for Stabilization of Discrete-Time Switched Positive Time-Varying Delay Systems with All Modes Being Unstable and Application to Uncertain Data

“…Next, Zhang and Sun [26] examined the practical exponential stability (ES) of discrete-time linear SPSs with impulse and AUMs. Moreover, An et al [28] investigated the robust exponential stabilization of SPSs with uncertainties based on the assumption that none of the individual modes is stabilizable. From the results in [20,26,28], it should be observed that the existence of the TVD was not taken into account in the systems.…”

“…Moreover, An et al [28] investigated the robust exponential stabilization of SPSs with uncertainties based on the assumption that none of the individual modes is stabilizable. From the results in [20,26,28], it should be observed that the existence of the TVD was not taken into account in the systems. Furthermore, there are beneficial results about switched positive time-varying delay systems (SPTVDSs) in cases in which all modes are unstable, reported briefly in the following.…”

Novel criteria for stability and ℓ1‐gain analysis of switched positive time‐delay systems

“…Switched positive systems are typically featured by switched systems with the positivity constraint on the state (and possibly input or output) variables. [1][2][3][4][5][6][7] In recent years, considerable attention has been attracted to the related exploration owing to the positive nature and their practical applications in numerous engineering practice, such as communication networks, 8 formation flying, 9 and compartmental systems. 10 This article, based on the non-negative state space, centers on devising the state-driven switching mechanism for switched positive time-delay systems, and simultaneously characterizes the mechanism by constructing the step-dependent multiple linear copositive Lyapunov-Krasovskii functionals (CLKF).…”

“…Switched positive systems are typically featured by switched systems with the positivity constraint on the state (and possibly input or output) variables 1‐7 . In recent years, considerable attention has been attracted to the related exploration owing to the positive nature and their practical applications in numerous engineering practice, such as communication networks, 8 formation flying, 9 and compartmental systems 10 .…”