Output-feedback H2∕H∞ consensus control for stochastic time-varying multi-agent systems with (x,u,v)-dependent noises

In this paper, the output feedback H2∕H∞ consensus control problem is investigated for discrete time-varying stochastic multi-agent systems with state, control and disturbance-dependent noises (also called (x,u,v)-dependent noises). Two new concepts for the H2 and H∞ consensus requirements are proposed to quantify the transient behavior of the consensus, over a finite horizon, for the addressed time-varying multi-agent systems. We aim to design an output feedback consensus controller such that the closed-loop multi-agent systems achieve the prescribed H2 and H∞ consensus performances over a finite horizon. By using the completing squares method and stochastic analysis techniques, sufficient conditions are derived for the existence of the desired output-feedback H2∕H∞ consensus controller in terms of the solution to two coupled backward recursive Riccati difference equations (RDEs). Moreover, an iterative algorithm is proposed for solving the RDEs by resorting to the Moore-Penrose pseudo inverse. A numerical example is utilized to illustrate the effectiveness of the proposed H2∕H∞ consensus control strategy.