Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems

Abstract

The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS) is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Guaranteed cost finite-time control of positive switched nonlinear systems with D-perturbation

“…Under the controller u(t) = K σ(t) y(t) the corresponding closed-loop system is given by (27)- (29) and the following inequalities hold:…”

“…In [26], the problem of robust nite-time guaranteed cost control for a class of impulsive switched systems with time-varying delay was studied. Very recently, [27] and [28] considered the guaranteed cost nite-time control for positive switched linear systems, [29] studied the guaranteed cost nite-time control for fractional-order positive switched systems. However, the problem of guaranteed cost nite-time control for positive switched nonlinear systems is still open, because nonlinear system is more complex than the linear system and there is a lack of e ective methods.…”

Guaranteed Cost Finite‐Time Control of Discrete‐Time Positive Impulsive Switched Systems

“…These results mainly focus on nonpositive systems. Very recently, in [28], guaranteed cost finite-time control was extended to fractional-order positive switched systems and a cost function for fractional-order positive systems (or fractional-order positive switched systems) was proposed. In [29], the problem of guaranteed cost finite-time control for positive switched linear systems with time-varying delays was considered and a cost function of positive systems (or positive switched systems) was also presented.…”

Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems

“…Only a few results about fractional-order positive switched systems have been presented [21][22][23]. [21] considered the controllability of FOPSS for fixed switching sequence.…”

“…[22] considered the the problem of state-dependent switching control of FOPSS. [23] considered the guaranteed cost finite-time control of fractional-order positive switched systems. However, to the best of our knowledge, there is no result on the control problem of GES and stabilization for FOPSS with ADT, which motivates our study.…”