Stability analysis and synthesis of fuzzy singularly perturbed systems

In this paper, we investigate the stability analysis and synthesis problems for both continuous-time and discrete-time fuzzy singularly perturbed systems. For continuous-time case, both the stability analysis and synthesis can be parameterized in terms of a set of linear matrix inequalities (LMIs). For discrete-time case, only the analysis problem can be cast in LMIs, while the derived stability conditions for controller design are nonlinear matrix inequalities (NMIs). Furthermore, a two-stage algorithm based on LMI and iterative LMI (ILMI) techniques is developed to solve the resulting NMIs and the stabilizing feedback controller gains can be obtained. For both continuous-time and discrete-time cases, the reduced-control law, which is only dependent on the slow variables, is also discussed. Finally, an illustrated example based on the flexible joint inverted pendulum model is given to illustrate the design procedures.