Local Synchronization of Linear Multi-Agent Systems Subject to Input Saturation

Abstract

: This paper is concerned with local state synchronization of linear agents subject to input saturation over a fixed undirected communication graph. The author first derives a sufficient condition for locally achieving the synchronization via a relative state feedback control law. Based on this analysis result, the author presents a linear matrix inequality (LMI) condition for designing the synchronizing state feedback gain. The present LMI condition is scalable as long as the eigenvalues of the associated graph Laplacian are available, and is efficiently solved by an existing convex programming algorithm.

Robust Consensus Analysis and Design Under Relative State Constraints or Uncertainties

“…Remark 4: As stated in the introduction, our method to derive LMI problems (21) and (28) for the Lur'e network (20) is more general than the method for a similar Lur'e network in [11]. On the other hand, the problem setting in this paper is in a different form of Lur'e networks with that in [13].…”

“…which is directly calculated from (11). Thus, the interesting result of Theorem 1 is that the distributed robust consensus design (13) …”

“…In other researches, [11]- [13] derived global consensus under input or state constraints by reformulating the constrained MAS as a network of Lur'e systems and employing Lyapunov theory. The paper [11] considered linear agents with input saturation but agents' dynamics is limited to be singleinput.…”

“…In other researches, [11]- [13] derived global consensus under input or state constraints by reformulating the constrained MAS as a network of Lur'e systems and employing Lyapunov theory. The paper [11] considered linear agents with input saturation but agents' dynamics is limited to be singleinput. Next, [12] and [13] investigated consensus problems for general linear MASs where outputs of agents are incrementally bounded or passive and obtained sufficient conditions for global consensus in the form of LMI convex problems.…”

“…Next, the transformed MAS is rewritten as a network of Lur'e systems and the robust stabilization problem is formulated as a distributed convex LMI problem. In comparison with the one in [11] for a similar type of Lur'e networks, our LMI problem is less conservative that: (i) employs a more general method namely the S-procedure; (ii) gives an exponential convergence to consensus instead of asymptotic convergence. Furthermore, our consensus controller gain is much more general than the diagonal one in [14].…”