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.
Highlights
Positive switched systems are a class of dynamics whose state and output are nonnegative whenever the initial conditions and inputs are nonnegative
Some researchers focus on finite-time stability (FTS) of positive switched systems: that is, given a bound on the initial condition, the system state does not exceed a certain threshold during a specified time interval
input-output finite-time stable (IO-FTS) involves signals defined over a finite-time interval and does not necessarily require the inputs and outputs to belong to the same class, and IO-FTS constraints permit specifying quantitative bounds on the controlled variables to be fulfilled during the transient response
Summary
Positive switched systems are a class of dynamics whose state and output are nonnegative whenever the initial conditions and inputs are nonnegative. The main contributions of this paper are as follows: (1) the positivity of positive switched systems with time-varying and distributed delays is proved; (2) the definition of IO-FTS is for the first time extended to positive switched systems with time-varying and distributed delays; (3) by using multiple copositive type Lyapunov function and MDADT approach, a state feedback controller is designed and sufficient conditions for IO-FTS of the corresponding closed-loop system are given. Such conditions can be solved by linear programming. Matrices are assumed to have compatible dimensions for calculating if their dimensions are not explicitly stated
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