Non-smooth fixed-time state feedback stabilization of uncertain switched systems with output constraints

Abstract

In this paper, non-smooth fixed-time state feedback stabilization of output-constrained uncertain switched systems has been investigated. First, to deal with the output constraints implicitly, a tangent-type barrier Lyapunov function ($T_{an}$-BLF), which degenerates into a quadratic function as the output constraints tend to infinity, is constructed deliberately. Then, the fixed-time state feedback control scheme for the output-constrained uncertain switched systems is established with remoulding the technique called adding a power integrator (AAPI). The upper bound of the settling time does not depend on the initial state and the arbitrarily small settling time can be obtained by just adjusting the specific parameters. The proposed method is operated in a unified framework, because it can tackle the cases for the uncertain switched systems with/without output constraints without requiring changes of switched controllers structure. At last, the effectiveness of the method is verified by a numerical simulation and a two-tank liquid-level system.