Stability analysis and feedback stabilization of bimodal piecewise linear systems

This thesis deals with the quadratic stability and feedback stabilization problems for continuous bimodal piecewise linear systems. First, we provide necessary and sufficient conditions in terms of linear matrix inequalities for quadratic stability and stabilization of this class of systems. Later, these conditions are investigated from a geometric control point of view and a set of sufficient conditions for feedback stabilization are obtained. Moreover, we consider observer design procedure for bimodal systems and we propose a simpler procedure by reducing the required conditions on the design. Finally, the result for stability anaylsis is extended to the bimodal systems with norm-bounded uncertainties and is proposed a corollary to guarantee the robust stability for the related systems.