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Finite-time control of uncertain fractional-order positive impulsive switched systems with mode-dependent average dwell time. (English) Zbl 1427.93085

Summary: This paper is concerned with the problem of finite-time control of uncertain fractional-order positive impulsive switched systems (UFOPISS) via mode-dependent average dwell time (MDADT). The uncertainties refer to interval and polytopic uncertainties. Firstly, the proof of the positivity of UFOPISS is given. By constructing linear copositive Lyapunov functions, the finite-time stability (FTS) of autonomous system with MDADT is studied. Then, state feedback controllers are designed to guarantee the FTS of the resulting closed-loop system with interval and polytopic uncertainties, respectively. All presented conditions can be easily solved by linear programming. Finally, a fractional-order circuit model is employed to illustrate the effectiveness of the proposed method.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
34A08 Fractional ordinary differential equations
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C41 Control/observation systems with incomplete information
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