Robust H_∞ control for T–S fuzzy systems with time-varying delay

Abstract

This article focuses on the problem of robust H _∞ control for uncertain T–S fuzzy systems with time-varying delay. By employing a novel technique, new delay-dependent stabilisation conditions for the existence of a robust H _∞ controller are obtained based on the parallel distributed compensation method. The result obtained is an important contribution as it establishes a new way that can reduce the conservatism without imposing any restrictions and computational efforts at the same time. In this article, all the conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using LMI optimisation techniques. Two numerical examples are given to demonstrate the merits of the approach proposed in this article. Finally, application to control a truck-trailer is also given to demonstrate the effectiveness of the proposed design method.

Keywords:

• LMI parallel distributed compensation
• H _∞ control
• Lyapunov–Krasovskii functional
• T–S fuzzy systems
• stabilisation
• time-delay systems
• robust control

Notations:

• W + W ^T is denoted as W + (*) for simplicity