Study On Control For Descriptor T-S Fuzzy Systems With Time-Domain Constraints

Time-domain hard constraints are probably the most widely existent in practice control systems. It is well recognized that performance requirements for control systems imply large control actions(and/or large system responses). All of these result in the conflict between high performance and satisfaction of time-domain hard constraints. If one ignores these constraints and only performance is treated, control action will exceed the bounds greatly. In such case, performance of closed-loop system wouldn't be guaranteed, even ofstability. So time-domain hard constraints must be handled in some control system design. Based on the descriptor Lyapunov theorem and the ellipsoidal invariant sets methods, by using linear matrix inequalities (LMIs), the dissertation studies stability problems and designs of controller for descriptor T-S fuzzy systems with time-domain hard constraints.In this paper, the optimal regulation problem and H_∞control problem for descriptor T-S fuzzy systems have been considered.Considering the optimal regulation problem for constrained descriptor T-S fuzzy system with non-zero initial state, we choose the energy of output as performance function, is the common super-bound for the performance and an ellipsoidal invariant set. So the optimal control can be realized by minimizing bound, and sufficient conditions dependent on the invariant set for satisfying time-domain hard constraints are derived.We then consider the L₂-gain disturbance attenuation problem for descriptor T-S fuzzy systems with time-domain hard constraints by state-feedback. We first seek an ellipsoidal set which includes initial state. Then, under the bound assumption of the disturbance energy, we seek another ellipsoidal set containing all possible perturbed trajectories. Finally the time-domain hard constraints can be enforced and translated into LMI conditions, which are also the scheme defined as double-ellipsoidal-set scheme. The designed controller can guarantee the satisfaction of constraints with the disturbance energy under a certain bound.