Local feedback Pareto strategy for weakly coupled large-scale discrete-time stochastic systems

Abstract

In this study, the author discusses a Pareto strategy implemented via state and static output feedback for a class of weakly coupled large-scale discrete-time stochastic systems with state- and control-dependent noise. The asymptotic structure along with the uniqueness and positive semi-definiteness of the solutions of cross-coupled non-linear matrix equations (CNMEs) is newly established via the implicit function theorem. The main contribution of this study is the proposal of a parameter-independent local state and static output feedback Pareto strategy. Moreover, a computational approach for solving the CNMEs is also considered if the information about the small parameter is available. Particularly, a new iterative algorithm based on the linear matrix inequality is established to design a Pareto strategy. Finally, in order to demonstrate the effectiveness of the proposed design method, a numerical example is provided for practical aircraft control problems.