On Decentralized Stabilization of Discrete-time Nonlinear Systems

This paper deals with stabilization of interconnected discrete-time nonlinear systems under given, arbitrary information constraints on the controller structure. As a prominent example, the considered information constraints on the controller structure include decentralized and distributed control over a given communication network. The main contribution of this paper is twofold. Firstly, we introduce the notion of structured control Lyapunov functions (CLFs) as a suitable tool for stabilizing controller synthesis under information constraints. This includes the relaxation of Lyapunov conditions at the local level. Secondly, we present a method for constructing structured CLFs and we show that the controller synthesis problem using structured CLFs can be formulated as a convex optimization problem. Possible solutions for solving this problem efficiently under several different types of information constraints are also indicated.