Unified and Nonconservative Stability Conditions for Continuous-Time Switched Systems

This article studies nonconservative stability conditions of continuous-time switched linear systems under mode-dependent dwell time (MDT). To establish a unified analysis approach for switched systems with stable and/or unstable subsystems, a concept called “dictionary” is introduced to characterize admissible MDT switching sequences. Subsequently, two equivalent nonconservative conditions of the global uniform asymptotic stability (GUAS) are obtained based on quadratic Lyapunov functions (LFs). Moreover, the stability results are transformed into convex conditions for facilitating the controller design. In addition, the developed stability results are applied to $L_{2}$ -gain analysis and $H_{\infty }$ controller design for the continuous-time switched linear system subject to external disturbances. Simulations are provided to validate the effectiveness and the superiority over existing results.