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In this article, the bipartite containment control problem is considered for discrete-time linear descriptor multi-agent systems (DMASs) with multiple dynamic leaders under fixed signed digraph topology, in which each leader can be autonomous or evolving dynamically via communicating with other leaders in its neighbourhood. Based upon the properties of the solutions to discrete-time modified generalised algebraic Riccati equations(MGAREs), three different types of distributed observer-based protocols utilising only available local information are devised. Algorithms for constructing the devised protocols are also presented. Moreover, sufficient conditions ensuring the bipartite containment of the DMASs are established. Finally, the effectiveness of the presented protocols is validated by numerical simulations. [ABSTRACT FROM AUTHOR]

This article investigates the controllability for a class of piecewise nonlinear impulsive non‐autonomous systems. The problem is addressed by considering the nonlinearities and impulses as perturbations. First, a standard framework is introduced to transform the issue of controllability to the existence of a fixed point by designing a proper admissible control and constructing a nonlinear operator on a Banach space. Then, two sufficient controllability conditions for such systems are developed by employing Schauder's and Rothe's fixed point theorems when the perturbations satisfy several nonlinear constraints including linear/sublinear growth conditions, bounded constraints, and Lipschitz conditions. It is shown that the controllability of such systems is influenced by the linear parts, the nonlinear perturbations, and the impulsive effects. Finally, the established controllability results are verified through several numerical examples. [ABSTRACT FROM AUTHOR]

A great deal of stabilization criteria has been obtained from study of stabilizing interconnected systems. The results obtained are usually based on continuous systems by state feedback. In this paper, decentralized impulsive control is presented to stabilize a class of uncertain interconnected systems based on Lyapunov theory. The system under consideration involves parameter uncertainties and unknown nonlinear interactions among subsystems. Some new criteria of stabilization under impulsive control are established. Two numerical examples are offered to prove the effectiveness and practicality of the proposed method.