| A switching system is a type of a hybrid system, consisting of continuous and discrete dynamical systems. It has many applications in various contexts such as automotive engine control, telecommunication, and congestion control of the internet. Since a switching system deals with a finite number of subsystems (continuous dynamics) and switches the subsystems according to a switching rule (discrete dynamics), its stability analysis will not be the same as that of a single continuous or discrete dynamical system. In this thesis, we investigate linear switching systems with delayed feedback control. Hence, the main focus of the work is to establish stability criteria for switching systems with delay.; In our stability investigation we use three different approaches for three different types of switching systems: single Lyapunov functional and function method for switching systems where all subsystems are unstable, multiple Lyapunov functional and function method for systems where all subsystems are stable and average dwell time method for systems having both stable and unstable subsystems. To study the effect of delay we use a Riccati type Lyapunov functional and the Razumikhin formalism for Lyapunov function. With these tools we are able to quantify the maximum time delay which guarantees stability of the switching system. The application to a feedback controlled reservation-based real-time CPU scheduler is discussed. |
