Sliding mode control and estimation for systems with mismatched uncertainties described by polytopic models.

The problem of designing variable structure systems with sliding modes for uncertain continuous-time plants involving mismatched parametric uncertainties and matched uncertainties, nonlinearities and/or disturbances is addressed in this thesis. Sliding mode control and estimation schemes are proposed for this class of plants. Pull and partial state information cases are considered. The latter scenario corresponds to sliding mode controllers using only measurable output signals, and comprises static and dynamic output feedback approaches. The proposed synthesis frameworks are based on linear matrix inequality methods and involve polytopic models. The multi-model paradigm is also explored to study the use of a finite set of Lyapunov matrices instead of a single Lyapunov matrix. Thus, a wider number of systems and control engineering problems can be dealt with. Control strategies using only measurable output signals are proposed for designing a single sliding mode controller for the simultaneous stabilisation of a finite collection of plant models. Design methodologies for sliding mode static and dynamic output feedback controllers based on linear matrix inequalities are described. The problem of state reconstruction using a discontinuous observer with sliding modes for systems with matched and mismatched parametric uncertainties is also studied in this dissertation. The mismatched uncertain component is considered as a disturbance whose effect on the output estimation error has to be minimised. The observer gain is synthesised by solving a convex optimisation problem involving linear matrix inequalities, with a polytopic description of the reduced-order error system, in terms of H performance. A detailed stability analysis is carried out for the sliding mode observer and the class of uncertain systems considered. Throughout this thesis, several design examples illustrate the proposed sliding mode control and estimation schemes, and computer simulations are used to demonstrate their efficacy.