Finite-time H∞ control for switched nonlinear systems

This paper studies the problem of finite-time control for switched nonlinear systems (SNSs), where the powers of chained integrators associated with individual subsystems can be different positive odd rational numbers from each other. First, the notion of finite-time for switched systems, as a performance index, is introduced. Contrary to the classical control, finite-time stability rather than asymptotic stability or practical stability needs to be satisfied in the finite-time control. Moreover, based on the method of multiple Lyapunov functions (MLFs) and the technique of adding a power integrator, a sufficient condition guaranteeing the solvability of the finite-time control problem for the system under consideration is derived via a designed switching law, where there is no subsystem whose corresponding control problem must be solvable. Finally, the effectiveness of the provided control strategy is demonstrated via a simulation example.