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This paper is dedicated to proposing improved input‐to‐state stability (ISS) criteria for a class of continuous‐time time‐varying switched singular systems (CTSSS) under slow/fast/slow‐fast switching signals. Specifically, for a CTSSS with time‐varying singular matrices, the authors start with an improved sufficient condition for verifying its ISS under slow switching signals based on the average dwell time method and a relaxed multiple Lyapunov function. Then, considering several or all subsystems may destroy the overall ISS, relaxed sufficient conditions are presented to ensure the ISS of the CTSSS under fast switching signals and slow‐fast switching signals, respectively. Note that the improvement of the proposed ISS criteria is embodied in the derivative of the required multiple Lyapunov functions along with the state trajectories of CTSSS can be positive or negative. Finally, three numerical examples are provided to illustrate the feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with necessary and sufficient conditions for stabilisability of time‐varying discrete‐time switched systems. Starting with an asymptotically stable function, an exponentially stable function and a uniformly exponentially stable function, we successively propose necessary and sufficient conditions for asymptotic stabilisability, exponential stabilisability and uniform exponential stabilisability of time‐varying switched linear systems. Further, considering the broad applications of finite‐time stability in practical systems, based on an additionally introduced concept of finite‐time stable functions, we derive a necessary and sufficient condition for finite‐time stabilisability of time‐varying switched linear systems. Afterwards, three illustrative examples are given to show the applicability of our theoretical results. In the end, we further discuss the necessary and sufficient conditions for global exponential stabilisability and global uniform exponential stabilisability of time‐varying switched non‐linear systems. Compared to traditional difference Lyapunov inequalities, we release the requirement on negative definiteness of the time‐difference of Lyapunov functions. [ABSTRACT FROM AUTHOR]