Output-feedback stabilisation for a class of switched nonlinear systems with unknown control coefficients

Abstract

This article investigates the problem of global stabilisation for a class of switched nonlinear systems with unknown control coefficients by output feedback. Full state measurements are unavailable. We first show that via a coordinate transformation, the unknown control coefficients are lumped together and the original switched nonlinear system is transformed into a new switched nonlinear system for which control design becomes feasible. Second, for the new switched nonlinear system, based on backstepping, we design output-feedback controllers for subsystems and construct a common Lyapunov function, which rely on the designed state observer, to guarantee asymptotic stability of the closed-loop system under arbitrary switchings. Finally, as an application of the proposed design method, global stabilisation of a mass-spring-damper system is achieved by output feedback.

Keywords:

• output feedback
• switched nonlinear systems
• mass-spring-damper system
• backstepping
• common Lyapunov function

Acknowledgements

This work was supported by the Chinese National Fundamental Research Programme under Grant 2009CB320601 and the National Natural Science Foundation of China under Grants 61233002 and 61174073.