Model Reduction of Hybrid Systems

|Abstract: High-Technological solutions of today are characterized by complex dynamical models. A lot of these models have inherent hybrid/switching structure. Hybrid/switched systems are powerful models for distributed embedded systems design where discrete controls are applied to continuous processes. Hybrid systems are also an important modeling class for nonlinear systems because a wide variety of nonlinearities are either piecewise-affine (e.g., a saturated linear actuator characteristic) or can be approximated as hybrid systems. The complexity of verifying and assessing general properties of hybrid systems, designing controllers and implementations is very high so that the use of these models is limited in applications where the size of the state space is large. To cope with complexity, model reduction is a powerful technique. This thesis presents methods for model reduction and stability analysis of hybrid/switched systems. Methods are designed to approximate hybrid/switched systems to low order models which adequately describe the behavior of the switched systems. Three frameworks for model reduction of switched systems are proposed which are based on the notion of the generalized gramians. Generalized gramians are the solutions to the observability and controllability Lyapunov inequalities. In the first framework the projection matrices are found based on the common generalized gramians. This framework preserves the stability of the original switched system for all switching signals while reducing the subsystems of the switched systems. The first framework is computationally efficient due to the construction of a single projection for all subsystems. This framework is used for switched controller reduction and it is shown that the stability of the closed loop system is guaranteed to be preserved for arbitrary switching signal. To compute the common generalized gramians linear matrix inequalities (LMI's) need to be solved. These LMI's are not always feasible. In order to solve the problem of conservatism, the second framework is presented. In this method the projection matrices are constructed based on the convex combinations of the generalized gramians. However this framework is less conservative than the first one, it does not guarantee the stability for all switching signals. The stability preservation is studied for this reduction technique. The third framework for model reduction of switched systems is based on the switching generalized gramians. The reduced order switched system is guaranteed to be stable for all switching signal in this method. This framework uses stability conditions which are based on switching quadratic Lyapunov functions which are less conservative than the stability conditions …