2012 12th International Conference on Control, Automation and Systems Oct. 17-21, 2012 in ICC, Jeju Island, Korea Randomly occurring Leader-following Consensus criterion for Multi-agent systems with Communication delay Myeongjin Park 1 , Ohmin Kwon 1* , Juhyun Park 2 , Sangmoon Lee 3 and Kihoon Kim 1 1 School of Electrical Engineering, Chungbuk National University, Cheongju 361-763, Korea (Tel : +82-43-261-2422; E-mail: netgauss;madwind@cbnu.ac.kr) 2 Department ofElectrical Engineering, Yeungnam University, Kyongsan 712-749, Korea (Tel : +82-53-810-2491; E-mail: jessie@ynu.ac.kr) 3 Department of Electronic Engineering, Daegu University, Gyungsan 712-714, Korea (Tel : +82-53-850-6647; E-mail: moony@daegu.ac.kr) Abstract: This paper proposes new delay-dependent leader-following consensus criterion for multi-agent systems with time-varying delays. Specially, the randomly occurring connection information of leader is considered in the concerned system. By constructing a suitable Lyapunov-Krasovskii functional and utilizing reciprocally convex approach, new delay-dependent consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effec- tiveness of the proposed method. Keywords: Randomly occurring leader; Consensus; Multi-agent systems; Time-delay; Lyapunov method. 1. INTRODUCTION Multi-agents systems (MASs) have received a great deal of attention due to their extensive applications in many fields such as biology, physics, robotics and control engineering, and so on. A prime concern in this system is the consensus problem. This problem is the agreement of a group of agents on their states of leader by interac- tion. For more details, see the literature [1]-[4] and refer- ences therein. Furthermore, it has been paid attention by applications in vehicle systems [2] and networked con- trol systems [3], [4]. Specially, consensus problem with the a leader is called a leader-following consensus prob- lem or consensus regulation [5]-[8]. Song et al. [5] stud- ied the second-order leader-following consensus problem of nonlinear MASs with general network topologies. In particular, this paper addresses what kind of agents and how many agents should be pinned, and establishes some sufficient conditions to guarantee that all agents asymp- totically follow the leader. In [6], based on Riccati in- equality and Lyapunov inequality, the leader-following consensus problem for MASs with both fixed and switch- ing interaction topologies were considered. Also, the ro- bust analysis of MASs with communication noise was in- vestigated. Chen and Lewis [7] derived distributed con- troller of a leader-follower network in the presence of communication delays. Moreover, in [8], distributed out- put regulation of leader-following MASs were purposed. This research is motivated by many practical problems including the target location estimation in a sensor net- work, and the synchronization of networked agents with the disturbance. However, to the best of author’s knowl- edge, the delay-dependent randomly occurring leader- This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0009273). * Corresponding author. following consensus analysis of MASs with time-varying delays has not been investigated yet. Since the finite speed of information processing, it is well known that time-delay often causes undesirable dynamic behaviors such as oscillation and instability of the system. Here, analyzing the consensus problem of the MASs with time- delay is identical to investigating the asymptotical stabil- ity of ones. The stability criterion for time-delay systems can be classified into two types: delay-dependent ones and delay-independent ones. The former are generally less conservative then the latter because that the delay- dependent stability criterion include the information of delay [9]. Motivated by the above discussions, we propose new delay-dependent randomly occurring leader-following consensus criterion for MASs with time-varying delays. By constructing a suitable Lyapunov-Krasovskii func- tional and utilizing reciprocally convex approach [10], new consensus criterion are derived in terms of LMIs which can be formulated as convex optimization algo- rithms which are amenable to computer solution [11]. One numerical example is included to show the effective- ness of the proposed method. Notation: R n is the n-dimensional Euclidean space, R m×n denotes the set of m × n real matrix. For sym- metric matrices X and Y , X>Y (respectively, X ≥ Y ) means that the matrix X - Y is positive definite (respec- tively, nonnegative). X ⊥ denotes a basis for the null- space of X. X T denotes the transposition of X. I de- notes the identity matrix with appropriate dimensions. k·k refers to the Euclidean vector norm and the induced matrix norm. diag{···} denotes the block diagonal ma- trix, respectively. E{x} and E{x|y} denote the expecta- tion of x and the expectation of x conditional on y, re- spectively. 883