Summary This paper discusses the observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinear terms. Firstly, based on the Luenberger‐like observer, by using the average dwell time approach, sufficient conditions are proposed to make closed‐loop systems be regular, be causal, as having a unique solution, and be uniformly finite‐time bounded. Then, a new linear matrix inequality sufficient condition for the existence of an observer‐based controller is obtained by using certain matrix decoupling techniques, and the controller is designed. In this paper, the conditions proposed not only give the observer‐based controller design methods but also guarantee the existence and uniqueness of solution for the systems. Since the quadratically inner‐bounded nonlinearities are more general than Lipschitz nonlinearities and one‐sided Lipschitz nonlinearities, compared with previous works, the proposed controller design methods in this paper are also more general than the existing ones. Finally, numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper.

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This paper studies the output regulation problem for switched singular systems based on an error feedback controller, where the system is influenced by a switched external system. Through the state coordinate transformation, the issue is transformed into the asymptotic stability problem of switched singular systems with autonomous subsystems. By introducing slack variables, solvable conditions including regulator equations and matrix inequalities are developed under average dwell time switching. It is worth mentioning that the solutions of the regulator equations are represented under some basic assumptions. Based on that and by utilizing the Finsler's lemma, less-conservative linear matrix inequality (LMI) conditions for the existence of the reduced-order controllers are obtained and the controller design methods are proposed. Finally, two examples are provided to test the correctness of the approaches we propose.