In the last two decades, the importance of switched systems either in modeling systems or in designing controllers has been growing. Like other control systems, the stability and -gain issues have a special role in analysis of switched systems, although the analysis for switched systems is much more complicated than the one for the other types of systems. For example, a switched system made of two stable subsystems can be unstable. A part of the thesis is devoted to explain applications of switched systems, how to type="#_x0000_t75" -gain are discussed for three main type="#_x0000_t75" -gain of a state-dependent switched system is introduced and proved. Furthermore, a switching algorithm is introduced, which is able to provide -stability for a switched system consisting given subsystems. Computing the Lyapunov functions for control systems has always been attracting. Many publications on calculating Lyapunov functions for switched systems concern the linear switched systems. In order to compute Lyapunov functions for a special Key Words : switched systems, stability, -gain, common Lyapunov function, multiple Lyapunov functions, sum of squares tool
