Unified and Nonconservative Stability Conditions for Continuous-Time Switched Systems
针对连续时间切换线性系统，引入“字典”概念刻画允许的切换序列，基于二次Lyapunov函数得到全局一致渐近稳定的两个等价非保守条件，并应用于L2增益分析和H∞控制器设计。
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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>-gain analysis and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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.