Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

Abstract

The problem of input-output finite-time control of positive switched systems with time-varying and distributed delays is considered in this paper. Firstly, the definition of input-output finite-time stability is extended to positive switched systems with time-varying and distributed delays, and the proof of the positivity of such systems is also given. Then, by constructing multiple linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a state feedback controller is designed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is input-output finite-time stable (IO-FTS). Such conditions can be easily solved by linear programming. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

L1 Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

“…If A bp � 0, then system (1) is turned into the system in [13]. If (1) is transformed into the systems in [21,22]. Moreover, if m 1 � m 2 � m 3 � m 4 � 1 and A bp � A dp � 0, then system (1) will be turned into the systems in [6,10,17,23].…”

“…It is noteworthy that the concept of IO-FTS is different from that of inputoutput stability, the later deals with the behavior of a system within an infinite time interval. As we know, only a few results considered the IO-FTS problem of positive switched linear systems [20][21][22]. Reference [20] extended IO-FTS to positive switched linear systems with state delays, but the time-varying delay and distributed delay were not considered.…”

“…Reference [20] extended IO-FTS to positive switched linear systems with state delays, but the time-varying delay and distributed delay were not considered. References [21,22] discussed the input-output finite-time control problem of positive switched systems and uncertain positive impulsive switched systems, respectively. However, for positive switched nonlinear systems, the IO-FTS problem has not been studied.…”

“…In this paper, we are interested in the problem of L 1 IO-FTS for a class of positive switched nonlinear systems with time-varying and distributed delays via ADT. e proposed system model is more general such that the systems dealt with in [6,13,17,[21][22][23] can be regarded as special forms.…”

Input–Output Finite Time Stabilization of Time-Varying Impulsive Positive Hybrid Systems under MDADT

“…Actually, the study of positive switched systems is more challenging than that of general switched systems because the features of positive systems and the features of switched systems have to be combined to obtain elegant results [20]. It should be pointed out that many previous results on positive switched systems focus mainly on stability analysis and controller synthesis [21][22][23][24][25][26][27][28][29], such as exponential stability [21][22][23][24][25], asymptotic stability [26], finite time stability (FTS) [27,28], and input-output finite time stability (IO-FTS) [30].…”