This paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed (NSP) systems with guaranteed H∞ control performance. We use the Takagi-Sugeno (T-S) fuzzy model to construct the singularly perturbed fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. At first, a set of common positive-define matrices and the controller gains are determined by the Lyapunov stability theorem and linear matrix inequality (LMI) approach. Then, a sufficient condition is derived for the robust stabilization of NSP systems. The composite fuzzy control will stabilize the original NSP systems for all ε ε (0, ε*) and the allowable perturbation bound ε* can be determined via some algebra inequalities. A practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computational Theory and Mathematics
- Artificial Intelligence
- Applied Mathematics