Robust guaranteed cost consensus for high‐order discrete‐time multi‐agent systems with parameter uncertainties and time‐varying delays

Abstract

The robust guaranteed cost consensus problem of high-order discrete-time linear multi-agent systems (MASs) with parameter uncertainties and time-varying delays is studied, and a linear consensus protocol of it is designed. Norm-bounded uncertainties and polytopic uncertainties are considered. First, the idea of robust guaranteed cost control is introduced into consensus problems for the MASs, where a cost function is defined based on state errors among neighbouring agents and control inputs of all the agents. Second, by constructing suitable Lyapunov functions and using the stability theory of discrete-time linear systems, two sufficient linear matrix inequality conditions are derived to insure that high-order discrete-time linear MASs with the two types of parameter uncertainties and time-varying delays reach robust guaranteed cost consensus. At the same time, two upper bounds of the guaranteed cost function are also given. Third, convergence results are given as final consensus values of the MASs with parameter uncertainties and time-varying delays. Finally, two numerical comparisons are given to illustrate the correctness and availability of the theoretical results.