Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input

Abstract

The stabilisation problem for a class of Takagi–Sugeno (TS) fuzzy bilinear systems (FBSs) with time-varying state and input delays is investigated in this article. A fuzzy controller is designed to stabilise TS FBSs with time-varying state and input delays via the parallel distributed compensation method. Based on a Lyapunov–Krasoviskii function, the delay-dependent stabilisation conditions are proposed in terms of a linear matrix inequality to guarantee the asymptotic stabilisation of time-delay FBSs with disturbance input. Two numerical examples with delays in the state and input are given to demonstrate that the proposed stability condition is less conservative than some existing results. Finally, the validity and applicability of the proposed control scheme are successfully demonstrated in the control of a Van de Vusse reactor with delay.

Keywords:

• robust control
• Takagi–Sugeno fuzzy control
• fuzzy bilinear system
• time-delay
• input-delay

Acknowledgements

This work is supported by the National Science Council of Taiwan, under contract grant NSC99-2221-E-027-101- and NSC-100-2221-E-027-017.