Memoryless H_∞ controller design for switched non-linear systems with mixed time-varying delays

Abstract

This article deals with the H _∞ control problem for a class of switched non-linear systems with mixed time-varying delays. The novel features here are that the system in consideration is non-linear perturbation with discrete and distributed delays, the time-varying delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using Lyapunov–Razumikhin functional approach, new sufficient conditions for the H _∞ control with exponential stability constraint are derived in terms of the solution of Riccati-type equations. The approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution.

Keywords:

• H _∞ control
• switched system
• exponential stability
• non-linear perturbation
• time-varying delay
• Riccati equation

Acknowledgements

This article was supported by the National Foundation for Science and Technology Development, Vietnam. The author thanks the anonymous referees for valuable remarks and suggestions which allowed us to improve the article and also Dr L.V. Hien for simulation of the example.