witched systems are a class of hybrid dynamical systems consisting of a finite number of subsystems and a switching law that specifies which subsystem will be activated along a trajectory at each instant of time. This area has attracted a lot of attention recently because of numerous applications of switched control systems; such as the control of mechanical systems, process control, automotive industry, switching power systems, aircraft traffic control, and communication networks. Switched systems are categorized based on switching signals. Switching signals are classified into arbitrary signals, state dependent signals, and time dependent signals. This thesis focuses on control of switched systems under arbitrary switching signals, due to their compatibility with the control system models in many applications. To analyze the stability of switched linear systems under an arbitrary switching signal, two kinds of Lyapunov functions are used: Switched Lyapunov Function (SLF); and Common Quadratic Lyapunov Function (CQLF). To investigate the existence of a CQLF, the solvability of Lie algebra needs to be examined. Since the existence of a SLF is a weaker condition than the existence of a CQLF, the use of the SLF method has been increased for analyzing stability and designing a suitable controller with performance analysis. Although valuable research on the stability of switched systems has been published, there are only a few results regarding the performance of these systems. Thus, this dissertation investigates some procedures to obtain different performances for switched systems under arbitrary switching signals. However, in some cases a static controller alone is not sufficient and designing a dynamic controller is needed. Therefore, this thesis presents an output dynamic feedback procedure designed to satisfy four desired performances in discrete-time linear switched systems, using a switched Lyapanuv function. Four different performances include: General Quadratic Constraints (GQC), Bounds on the Peak to Peak Gain (G), Peak Impulse (PI), and Settling Time (ST). GQC minimizes the quadratic function of system’s inputs and outputs. G is an index which measures the peak amplitude of the output signal over the bounded input disturbance. PI or ST puts an upper bound on the peak impulse or bound on the settling time of output signal. According to the defined performances, the switched systems are analyzed and three theorems are introduced to provide sufficient conditions to satisfy the performances. Using these results, existence of proposed performances in the switched systems can be easily iected. Then output dynamic feedback controllers are designed to stabilize the switched closed-loop system, while satisfying the objectives, under arbitrary switching signals. The results are stated and proved in three designing theorems. The design procedures are presented in the form of Linear Matrix Inequalities (LMIs) which are solvable by using existing LMI-solvers such as YALMIP. Finally, simulation results are provided to demonstrate the effectiveness of the proposed methods. The results show noticeable improvements in these performances in comparison with previous studies which only have stabilized the switched systems. Keywords Switched discrete-time systems; Performance analysis; Arbitrary switching signal; Output dynamic feedback controller; LMI.