Multi-objective Control for T-S Fuzzy Singularly Perturbed Systems

Abstract

In this chapter, we consider the problem of multi-objective control for T-S fuzzy singularly perturbed systems. The problem consists of H _∞ control, pole placement and singular perturbation bound design. Specifically, given an H _∞ performance bound γ > 0, an LMI stability region $\textbf D$ and an upper bound ε ₀ for the singular perturbation parameter ε, we will construct an ε-dependent state feedback controller, such that ∀ ε ∈ (0, ε ₀], the L ₂-gain of the mapping from the exogenous input noise to the regulated output is less than or equal to γ and the poles of each subsystem are all within the LMI stability region $\textbf D$. Two sub-problems of the multi-objective control are discussed and the main problem is then solved. An ε-dependent state feedback controller is designed by solving a set of ε-independent LMIs. It is shown that the controller is well-defined ∀ ε ∈ (0, ε ₀]. If ε ₀ is sufficiently small, the controller can be reduced to an ε-independent one. At last, an inverted pendulum controlled by a dc motor via a gear train is used to illustrate the obtained approach.