Output feedback Fuzzy Guaranteed Cost Tracking Control Design for Nonlinear Time-Delay Systems

This paper is concerned with the problem of output feedback fuzzy guaranteed cost tracking control design for nonlinear time-delay systems with time-varying delay. Weassume that these nonlinear time-delay systems can be modeled by Takagi and Sugeno (T-S) fuzzy modeling scheme. Thecontroller is in a Parallel Distributed Compensation (PDC) form. The final controller should result in quadratic stability of the closed-loop nonlinear time-delay system and guaranteeingthe tracking error norm to some reference and bounded signals. Along with a few results in the literature, firstly wehave implemented a modified cost function. This new cost function includes tracking error norm together with the quadratic form of corresponding controller output. Theexisting results implement an observer-based output feedback structure for any local controller and offer a double stepprocedure to find the controllers and observers gains. We have taken a new form for the controller which has two extra terms with respect to ordinary delay –free systems. This new form of controller structure enables us to offer a single step Linear Matrix Inequality (LMI) method to find the output feedbackfuzzy guaranteed cost controller. Moreover, the optimal controller can be found by a convex minimization approach over the convex solution set.

Keywords:

Nonlinear systems , T-S fuzzy systems , output feedback , tracking control , guaranteed cost