Finite‐time non‐smooth stabilization of cascade output‐constrained switched systems

Abstract

Finite‐time non‐smooth stabilization of cascade output‐constrained switched systems via state feedback is investigated. The cascade switched systems consist of subsystems in general form with zero dynamics and mixed powers taken into account. To deal with the finite‐time stabilization problem of such kind of switched systems, some mild assumptions, input‐to‐state stability property of zero dynamics, an appropriate growth rate assumption on nonlinear terms and some well‐known conditions for small signals, have been imposed on subsystems. Then, state feedback controllers are constructed first by revamping adding a power integrator technique and finite‐time stability analysis of the resultant closed‐loop switched systems are implemented by the deliberately constructed tangent‐type barrier Lyapunov function (Tan$$ {T}_{an} $$‐BLF). Meanwhile, the output constraint of switched systems is also implicitly guaranteed by the Tan$$ {T}_{an} $$‐BLF. Switched systems discussed in this article can encompass almost all p$$ p $$‐normal ones because of the inclusion of zero dynamics, mixed powers, and the homogenous upper bounded assumption on nonlinear terms. And, the method proposed in this article operates in a unified framework to tackle finite‐time stabilization of switched systems because the constructed common Tan$$ {T}_{an} $$‐BLF degenerates into a quadratic function when the output constraint tends to infinity. Simulations are carried out to show the efficiency of the proposed method.

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