Adaptive Fixed‐Time Non‐Smooth Stabilization of Switched Systems With Output Constraints

ABSTRACT In this paper, the adaptive non‐smooth fixed‐time state feedback stabilization problem of output‐constrained switched systems are investigated. In order to well deal with the output constrains and uncertain parameters, a common barrier Lyapunov function which includes a tangent‐type term of the system state and a quadratic term of the uncertain parameter estimation error is constructed. Adaptive fixed‐time state feedback controllers and parameter update laws are designed by virtue of adding a power integrator technique with some mild assumption imposed on the subsystem's nonlinear terms. Simulation results of a numerical example and a two‐tank liquid‐level system presented in this paper explicitly demonstrate the effectiveness of the proposed approach in this paper. Subsystems powers considered in this article only need to be greater than zero, regardless of odd or even numbers, which make the structure of switched systems more general. The proposed method provides us to perform the design of the adaptive fixed‐time stabilizers for switched systems with/without output constraints simultaneously with the same controller structure, which means it has a unified nature.