Stability of non-diagonalizable switched linear systems on time scales.

This thesis investigates the stability of switched linear systems on time scales using Lyapunov stability theory. First, we focus on the most general case, nondiagonalizable systems with arbitrary switching. Subsequently, a constrained switching case is investigated. Several examples are given for both cases. Switched linear systems are often found wherever a dynamical system is coupled with supervisory control logic that can abruptly change the system's operating mode, such as in the transmission of a vehicle or on computer-controlled real-time networks. This coupling of a dynamical system with discrete logic is difficult to model on standard time domains, especially if the switching events are non-uniformly spaced. Time scales mathematics allows for these non-uniform time domains.