Controller design for T-S fuzzy singularly perturbed switched systems

This paper investigates the problem of fuzzy controller design for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. By using the average dwell time approach together with the piecewise Lyapunov function technique, a set of well-conditioned sufficient conditions for the existence of controller is proposed, under which the overall switched closed-loop system is asymptotically stable. A state feedback controller depending on the singular perturbation parameter ε, which is shown to work well for all ε ∈ (0, ε
₀
), where ε
₀
is the stability bound of singularly perturbed systems, is developed. In addition, when ε is sufficiently small, the ε-dependent controller can be reduced to an ε-independent one. Then, an ε-independent state feedback stabilization controller design method is proposed in terms of linear matrix inequalities. Furthermore, under the controller, the stability bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to show the feasibility and effectiveness of the obtained results.