In this paper, the problems of stability and stabilization are considered for a class of switched linear systems with slow switching and fast switching. A multiple convex Lyapunov function and a multiple discontinuous convex Lyapunov function are first introduced, under which the extended stability and stabilization results are derived with a mode-dependent average dwell time switching strategy, where slow switching and fast switching are exerted on stable and unstable subsystems, respectively. These two types of Lyapunov functions are established in a constructive manner by virtue of a set of time-varying functions. By using our proposed approaches, larger stability regions of system parameters are identified, and tighter bounds can be obtained for the mode-dependent average dwell time. New mode-dependent and time-varying controllers are constructed for a class of switched control systems with stabilizable and unstabilizable subsystems as well. All the stability and stabilization conditions can be given in terms of strict linear matrix inequalities (LMIs), which can be checked easily by using recently developed algorithms in solving LMIs. Finally, two numerical examples are provided to show the effectiveness of the obtained results compared with the existing results.

The work proposes the pre‐l2‐gain analysis framework based on the newly raised nonweighted pre‐l2‐gain performance index and predictive Lyapunov function, which is devoted to nonweighted l2‐gain analysis and relevant control of discrete‐time switched systems under mode‐dependent average dwell time. This also provides new ideas for other disturbance‐related studies. To begin with, the predictive Lyapunov function is established for switched nonlinear systems in the sense of better reflecting future system dynamics and future external disturbances. Hence, it is achievable to develop less conservative stability and nonweighted pre‐l2‐gain criteria for switched linear systems. Further, a new disturbance‐output expression is devised to match with the nonweighted pre‐l2‐gain, whose function is to estimate and optimize the traditional nonweighted l2‐gain of the underlying system through discussions. Then, a solvable condition is formulated to seek the piecewise time‐dependent gains of switching controller in a convex structure, ensuring the global uniform exponential stability with nonweighted pre‐l2‐gain and thereby attaining much smaller non‐weighted l2‐gain. Finally, the simulation comprised of a circuit system and a numerical example manifests the impressive potential of the obtained results for the purpose of preferable disturbance attenuation performances.

No abstract

No abstract