Regional stabilization and H_∞ control of time-delay systems with saturating actuators

A linear parameter varying approach is introduced for the design of a constant state-feedback controller that locally stabilizes linear systems with state time-varying delays and saturating actuators and achieves a prescribed performance level for all disturbances with uniformly bounded magnitudes. A polytopic representation is used to describe the saturation behaviour. Delay-dependent sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained for the existence of such a controller. An estimate is made of the domain of attraction for the disturbance-free system. The conditions for the stabilizability and H_∞ performance of the system apply the Lyapunov-Krasovskii functional and the recent descriptor approach to the control of time-delay systems, whereas the conditions for finding an ellipsoid that bounds the set of the states (in the Euclidean space) that are reachable from the origin in finite time are obtained via the Razumikhin approach. The resulting conditions are expressed in terms of linear matrix inequalities, with some tuning parameters, and they apply a different Lyapunov function to each of the vertex points that stem from the polytopic description of the saturation in the actuators.