Robust Stability Analysis of Discrete-Time Switched Linear Systems with Dwell Time and Mode-Dependent Dwell Time Switching

This paper investigates the robust asymptotic stability of discrete-time switched linear systems under dwell time and mode-dependent dwell time switching signals. At first, sufficient conditions are derived to determine a lower bound on the stabilizing dwell time and mode-dependent dwell time of switched linear systems. Meanwhile, a numerical method is provided to compute the optimized value of the proposed dwell time. Then, the obtained results for the stabilizing dwell time are extended to parametric switched linear systems with uncertain parameters belonging to known intervals. Finally, we determine a stability margin for uncertain parameters of the switched linear system with dwell time switching. To achieve this, an optimization algorithm is presented to estimate the maximal stability intervals of uncertain parameters. Illustrative examples are included to demonstrate the effectiveness of the results.