Robust Analysis and Synthesis of Uncertain Linear Hybrid Systems with Networked Control Applications

This dissertation investigates the robust analysis and control of uncertain hybrid systems, which are perturbed by time-variant parametric uncertainties and persistent disturbances. Three kinds of hybrid control problems are considered: robust tracking and regulation control, robust stabilization, and robust performance. For robust tracking and regulation control, the aim is to design hybrid control law so that all the trajectories starting from a given initial region in the state space can be driven to a specified target region while satisfying certain state and control constraints. This problem is solved by a backward reachability analysis approach, and a linear programming based model predictive control scheme. The problem of robust stabilization for uncertain hybrid systems is then formulated and studied in the framework of tracking and regulation control. Next, the persistent disturbance attenuation problems are considered for the uncertain hybrid systems. It is shown that the robust optimal disturbance attenuation control law can be implemented as piecewise linear state feedback. However, the difficulty is that the disturbance attenuation property analysis problem for general uncertain hybrid systems is undecidable. An important question is then to specify the decidable class for the robust performance analysis problem. It is proved that the robust analysis and synthesis procedures terminate in finite number of steps for switched linear systems under certain conditions. Switched linear systems represent an interesting subclass of hybrid systems with simplified discrete event dynamics. One of the most elusive problems in the switched system's literature has been the switching stabilizability problem, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. A necessary and sufficient condition for the asymptotic stabilizability of switched linear systems is introduced here, which is an improvement upon the sufficient only conditions found in the literature. Considering a class of applications, networked control systems(NCSs) with uncertain access delay and packet dropouts are studied in the framework of switched systems. The stability and disturbance attenuation properties of such NCSs are explored. In particular, two different switched system approaches are proposed. In the first approach, which is based upon the assumption that the access delay and consecutive packet dropouts are bounded, an arbitrary switching system model is obtained by incorporating all possible delay-dropout patterns and relaxing the switching signal to be arbitrary. Alternatively, the second approach is based on average dwell time concepts and restricts the occurring frequency and the number of dropped and delayed packets in the time average sense. In addition, a stability and L2 performance preserving network bandwidth management policy is proposed based on the average dwell-time approach.