Ao Dun

Design of controller for Lur'e systems guaranteeing dichotomy

In this paper, the problem of controller design for Lur’e systems guaranteeing dichotomy is investigated. On the basis of Kalman–Yakubovich–Popov (KYP) lemma and two frequency equalities, a new methodology for the dichotomy analysis of the Lur’e systems is proposed. A linear matrix inequality (LMI) based criterion is derived, which is equivalent to the Leonov’s frequency-domain one, while for the dichotomy analysis and synthesis which is more straightforward than the frequency-domain one. In virtue of this result, a dynamic output feedback controller ensuring the dichotomy property for Lur’e systems is designed. Finally a numerical example is included to demonstrate the validity and the applicability of the proposed approach.

Consensus of nonlinear dynamical networks with Markovian switching topologies and time-varying delay

This paper addresses the consensus problem for complex dynamical networks with each node being a Lure system whose nonlinearity satisfies a sector condition. Communication time-delay and Markovian switching topologies are also considered in the dynamical network system. The switching for topologies is determined by a Markov chain, each topology corresponding to a state of the Markov chain. The partial stability theory, Lyapunov-Krasovskii function and Schur complement formula are applied to get the novel criterion, which have the forms of bilinear matrix inequalities. Moreover, the method of designing a static output controller is provided. Finally, numerical examples are presented to illustrate the efficiency and applicability of the proposed methods.

Static output feedback control for H ∞ stability and consensus of nonlinear complex dynamical networks

This paper investigates the H∞ stability and consensus of uncertain discrete-time nonlinear complex dynamical network systems based on T-S fuzzy model. The nonlinear complex dynamical network system consists of N nonlinear discrete-time subsystems. Parallel distributed compensation algorithm and Lyapunov method are applied to design an H∞ decentralized fuzzy static output feedback controller. Based on Lyapunov method, a static output feedback controller is designed to guarantee that the closed-loop system is asymptotically H∞ stable. By considering the characteristic of interconnection matrix of the network, the test of the stability of the network system is separated in to the test of the stability of the several nonlinear systems. Furthermore, the consensus problem for the leader-follower complex dynamical network is considered. And the proposed criterion can be obtained by solving a set of linear matrix inequalities (LMIs) which are numerically feasible. The effectiveness of the proposed methods is demonstrated through numerical examples.

Static output controller design for consensus of dynamical networks with interconnections

This paper considers the consensus problems for complex dynamical network systems. For the dynamical network systems, more than one interconnections are considered in view of the fact that the subsystems of networks may be multiple interconnected. Sufficient and necessary conditions for consensus are given for the linear dynamical networks with state interconnections and controller interconnections. Moreover, a static output controller design method based on a parameter-dependent Lyapunov function is provided. Furthermore, multiple interconnected nonlinear dynamical network system is investigated, and the subsystems are Lure systems. Kalman-Yakubovich-Popov (KYP) lemma and the Schur complement formula are applied to get novel criteria, which have the forms of linear matrix inequalities (LMIs). And the test of the consensus of a network with Lure systems as its nodes is separated into the test of the absolute stability of several independent Lure systems. Finally, numerical examples are presented to illustrate the efficiency and applicability of the proposed methods.

Global convergence of a class of nonlinear dynamical networks

This paper considers the global convergence of a class of nonlinear dynamical networks, and the subsystems are discrete time pendulum-like systems. Different from most of the existing results, two kinds of interconnections are considered in view of the fact that the subsystems of networks may have more than one kind of interconnection between each other. The Kalman-Yakubovich-Popov (KYP) lemma and the Schur complement formula are applied to get novel criteria, which have the forms of linear matrix inequalities (LMIs). The Kronecker product is presented which can be used to handle a class of LMI problems. The test of the global convergence of a network of pendulum-like systems is separated into the test of the global convergence of several independent pendulum-like systems. Furthermore, a controller design method based on LMIs is provided. Finally, a numerical example is presented to illustrate the efficiency and applicability of the proposed methods.