Leader-Following Consensus Stability of Discrete-Time Linear Multiagent Systems with Observer-Based Protocols

Abstract

We consider the leader-following consensus problem of discrete-time multiagent systems on a directed communication topology. Two types of distributed observer-based consensus protocols are considered to solve such a problem. The observers involved in the proposed protocols include full-order observer and reduced-order observer, which are used to reconstruct the state variables. Two algorithms are provided to construct the consensus protocols, which are based on the modified discrete-time algebraic Riccati equation and Sylvester equation. In light of graph and matrix theory, some consensus conditions are established. Finally, a numerical example is provided to illustrate the obtained result.

Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer

“…In [26], the discrete-time leader-following consensus problem was investigated via the observer-based protocols under switching topologies. The full-order observer and reduced-order observer-based consensus protocols were provided in [24] to solve discrete-time leader-following consensus problem. In [5], the authors investigated H ∞ consensus problem for discrete-time multi-agent systems with general linear dynamics via dynamic output feedback method.…”

“…But the input u r (k) is regarded as a common policy, which is assumed to be known by all the following agents. In many references such as [9,16,24,29], u r is assumed to be u r = 0. The proposed reduced-order observer-based distributed consensus protocol for agent i concludes an observer with same form (5) and a feedback control law with form…”

“…To achieve consensus, it is necessary that the interaction topologyḠ contains a directed spanning tree with root v r . More discussion ofḠ and its covering circle can be referred to [24] By (26) and (28), we get the error dynamics for the closed loop system as…”

Consensus stability of discrete-time descriptor multi-agent systems

“…Furthermore, we know that there exists a covering circleC(1, r 0 ) with r 0 < 1 for matrix L + G d [12].…”

“…The distributed state-feedback protocols were proposed to solve discrete-time consensus with general linear dynamics systems by [9,10]. The observer-based consensus protocols for the discrete-time multi-agent systems has been addressed by [11,12,13]. The descriptor system is also referred to as singular statespace system, generalized system, or implicit system [14].…”