Dynamic output feedback controller synthesis for piecewise-affine systems

Increasing demands on performance for complex industrial engineering applications over wide operating regimes have caused control designers to move from linear to nonlinear controllers and to controllers that incorporate both discrete logic and continuous-time variables (such is the case of mode switching controllers). As a consequence, many of the currently developed control applications are logic-based and therefore incorporate both continuous-time and discrete-event state dynamics. However, traditional control theory has concentrated on analysis and control design for systems with either a continuous-time state or a discrete-event state. The new control applications have therefore resulted in the need to develop new analysis and synthesis methods. Based on the need expressed in the previous sentence, the objective of this work is to develop a new computer aided controller synthesis method for a class of complex dynamical systems. By complex we mean systems with multiple models, each model being valid in a given region of a certain space (e.g., the state space or some energy space), and systems involving mode switching between the different models. These systems have a state with hybrid nature that consists of both continuous-time physical variables and discrete-event logical variables. In that sense the complex systems considered in this work fall under the framework of hybrid systems. The work focuses mainly on an important subclass of hybrid systems: piecewise-affine systems (PWA). The thesis develops an approximate synthesis technique for both state and dynamic output feedback control of PWA systems. The synthesis method is only approximate in the sense that it is not guaranteed to work for all systems. However, when it works, the results are unambiguous and it yields a stabilizing feedback controller with exponential convergence rate guarantees.