Finite-time H_∞ control for switched nonlinear systems

Abstract

This paper studies the problem of finite-time $H_{\mathrm{\infty }}$ 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 $H_{\mathrm{\infty }}$ for switched systems, as a performance index, is introduced. Contrary to the classical $H_{\mathrm{\infty }}$ control, finite-time stability rather than asymptotic stability or practical stability needs to be satisfied in the finite-time $H_{\mathrm{\infty }}$ 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 $H_{\mathrm{\infty }}$ 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.

Keywords:

• Switched nonlinear systems
• finite-time $H_{\mathrm{\infty }}$ control
• multiple Lyapunov functions
• power integrator

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under grants 61773098 and 61773100 and the 111 Project (B16009).