Lurie Systems Research Articles

State estimation and synchronization of pendula systems over digital communication channels

The recent results on nonlinear systems synchronization and control under communication constraints are applied to the remote state estimation and synchronization for a class of exogenously excited nonlinear Lurie systems. State estimation of the chain of diffusively coupled pendulums over the digital communication channel with limited capacity is experimentally studied. Advantage of the adaptive coding procedure under the conditions of the plant model uncertainty and irregular disturbances is shown. Quality of the estimation is evaluated by means of the experiments with the multi-pendulum set-up. Experimental study of master-slave synchronization over network (local network, wireless network) for the system with two cart-pendulums is presented.

Nonlinear Consensus Algorithms with Uncertain Couplings

AbstractDistributed algorithms for synchronization and consensus in multi‐agent networks are considered. The agents are assumed to be linear of arbitrary order, the interaction topology may switch, and the couplings are uncertain, assumed only to satisfy certain quadratic constraints. Using the Kalman‐Yakubovich‐Popov lemma and absolute stability theory techniques, consensus criteria for the networks of this type are obtained. These criteria extend a number of known results for agents with special dynamics and are close in spirit to the celebrated circle criterion for the stability of Lurie systems.

Robust H∞ cluster synchronization analysis of Lurie dynamical networks

The cluster synchronization problem of complex dynamical networks with each node being a Lurie system with external disturbances and time-varying delay is investigated in this paper. Some criteria for cluster synchronization with desired H∞ performance are presented by using a local linear control scheme. Firstly, sufficient conditions are established to realize cluster synchronization of the Lurie dynamical networks without time delay. Then, the notion of the cluster synchronized region is introduced, and some conditions guaranteeing the cluster synchronized region and unbounded cluster synchronized region are derived. Furthermore, the cluster synchronization and cluster synchronized region in the Lurie dynamical networks with time-varying delay are considered. Numerical examples are finally provided to verify and illustrate the theoretical results.

Research on Impulsive Lurie Systems with Time-Delay

Based on stability theory of impulsive differential equation and new comparison theory of impulsive differential system, some simple yet less conservative criteria ensuring impulsive synchronization of the Lurie systems are derived. A numerical example is given to illustrate the effectiveness of the method.

Absolute stability analysis of neutral type Lurie system with unbounded distributed delay and interval time-varying probabilistic delay

In this paper, a novel stability criterion for the absolute stability of neutral type Lurie system with unbounded distributed and interval time-varying delay is proposed. The delay range is divided into two segments for stability analysis. The probability distribution of interval time-varying delay in the two segments is assumed to be known a priori. A tighter bounding technique is developed for the integral terms arising in the derivative of Lyapunov-Krasovskii functional (LKF). This bounding technique along with the Wirtinger inequality is used to develop the absolute stability criteria in terms of linear matrix inequalities. The proposed stability analysis has been further extended to the robust absolute stability of uncertain Lurie system of neutral type with mixed delays. The effectiveness of the proposed approach has been illustrated through numerical examples.

Accuracy of Fridman's estimates for sampling interval: nonlinear system case study

Abstract An attempt to evaluate accuracy of Fridman's sampling interval estimates for nonlinear discrete-continuous systems where the controlled plant belongs to a class of cascade passifiable Lurie systems. Numerical results obtained for master-slave configuration of two mobile robots demonstrate good accuracy of Fridman's estimates: error of the sampling interval estimate is less than 25% of the value obtained from extensive simulation. In contrast, the error obtained by conventional method from quadratic Lyapunov function is more than 75% of the value obtained from simulation.

Synchronization of Lurie system based on contraction analysis

In this paper, a new synchronization criterion for chaotic Lurie systems with sector and slope restricted nonlinearities is proposed. Without analyzing the stability of the error system, synchronization condition for general Lurie systems is firstly given based on the contraction analysis. Furthermore, the result is extended to the Chua’s system whose state equation is not differentiable. Finally, three representative examples are presented to support the theoretical results.

AUXILIARY ADAPTIVE MECHANISM IN CHAOS SYNCHRONIZATION: ESTIMATORS FOR LIPSCHITZ CONSTANT AND UPPER BOUND OF TIME-DELAY'S CHANGE RATE

Adaptive robust synchronization method is proposed for chaos synchronization of Lurie systems with time-varying delay. To weaken the restrictions on the change rate of time-varying delay in synchronization problems, adaptive estimations related to the derivative's upper bound of the time-varying delay are designed, so this upper bound can be unknown. The Lipschitz constant of the nonlinear link is also adaptively estimated, rather than being pre-calculated. Whole design is in the framework of robust control, and the synchronization can endure disturbance effectively. In addition, the synchronization of chaotic Lurie system with time-varying delay is realized as an example.

The Popov Criterion For Consensus Between Delayed Agents

Abstract We consider consensus algorithms for multi-agent networks with high-order and delayed dynamics of agents. The topology is assumed to be fixed and undirected, however the couplings may be nonlinear and uncertain, we assume only the symmetry condition to be valid. We obtain conditions of stability for such algorithms that are similar in spirit to the celebrated Popov criterion for the stability of Lurie systems.

The Circle Criterion for Synchronization in Nonlinearly Coupled Networks.

The problem of synchronization (consensus) in nonlinearly coupled network is addressed. The agents of the network are assumed to identical and linear, however, they may have arbitrary order and be unstable. The interaction topology may switch and the couplings are uncertain, assumed only to satisfy conventional quadratic constraints. We offer easily verifiable synchronization criteria, based on the Kalman-Yakubovich-Popov lemma and extending a number of known result for agents with special dynamics. Those criteria are close in spirit to the celebrated circle criterion for the stability of Lurie systems.

Consensus in switching networks with sectorial nonlinear couplings: Absolute stability approach

Consensus algorithms for multi-agent networks with high-order agent dynamics, time-varying topology, and uncertain symmetric nonlinear couplings are considered. Convergence conditions for these algorithms are obtained by means of the Kalman–Yakubovich–Popov lemma and absolute stability techniques. The conditions are similar in spirit and extend the celebrated circle criterion for the stability of Lurie systems.

Delay-dependent absolute stability criterion for Lurie system with probabilistic interval time-varying delay

In this paper, the absolute stability of Lurie control system with probabilistic time-varying delay is studied. By using a new extended Lyapunov-Krasovskii functional, an improved stability criterion based on LMIs is presented and its solvability heavily depends on the sizes of both the delay range and its derivatives, which has wider application fields than those present results. The efficiency and reduced conservatism of the presented results can be demonstrated by two numerical examples with giving some comparing results.

Synchronization of nonlinear Lurie systems on the basis of passification and backstepping

The problems of passification and synchronization of nonlinear systems are solved with the aid of the backstepping method for cascade systems of the Lurie type with functional uncertainty. Estimates of the errors caused by bounded disturbances and controller discreteness are given. The stated theorem is extended to the case of net systems. The obtained results are applied to the synchronization problem of movement of two mobile wheeled robots and are illustrated by way of computational modeling.

Delay-distribution-dependent Robust Stability Analysis of Uncertain Lurie Systems with Time-varying Delay

AbstractIn this paper, the problem of robust absolute stability of Lurie system with probabilistic time-varying delay and norm-bounded parametric uncertainty is considered. The time delay variation range is divided into two subintervals. By considering the probability distribution of the time-varying delay between the two subintervals and the knowledge of the delay variation range, a novel linear matrix inequalities (LMIs) based stability condition is derived by defining a Lyapunov Krasovskii functional. It is illustrated with the help of numerical examples that the derived stability criteria can lead to less conservative results as compared to the results obtained by the traditional method of using the delay variation range information only.

Adaptive synchronization of asymmetric coupled networks with multiple coupling delays

The synchronization problem of asymmetric networks with multiple coupled delays is investigated in this paper. By using Lyapunov stability theory and Lasalle's invariance principle, several synchronization criteria are deduced for both asymmetric networks with and without norm uncertainties. Furthermore, the synchronization problem of a special complex network with each node being a Lurie system is studied. The main results show that the states of all nodes of networks globally asymptotically synchronize to a desired synchronization state by designing suitable adaptive controllers, and these controllers have strong robustness against the uncertain coupling matrixes. Finally, several illustrative examples with numerical simulations are given to show the feasibility and efficiency of theoretical results.

The H-Infinity Stability of a Class of Lurie Switched Systems with Hybrid Dynamical Systems

The H- infinity stability of Lurie switched systems is investigated. All the subsystems are Lurie systems. Lyapunov functions is used to derive the sufficient conditions for H- infinity stability of systems .

The Problem of Absolute Stability of a Class of Lurie Switched Time-Delay Systems

The absolute stability problem of Lurie time-delays switched systems is investigated. All the subsystems are Lurie systems. Lyapunov functions is used to derive the sufficient conditions for the absolute stability of systems

Lr-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations

The synchronous control of a class of disturbed chaotic Lurie systems is probed in. The conception of L r -synchronization of drive–respond systems is presented. Via Lyapunov function analysis and comparison principle, L r synchronous controller of the drive–respond systems under perturbation is given and its robustness is also discussed. Barbalat lemma is further used to derive the adaptively synchronous controller for the unknown disturbance situation and the globally asymptotical synchronization is realized. All designed controllers are verified by the simulations and the given controllers are linear, which are convenient and can produce rapid convergence speed of the error systems.

Improved Stability Criteria for Lurie Type Systems with Time-varying Delay

In this technical note, we present a new stability analysis procedure for ascertaining the delay-dependent stability of a class of Lurie systems with time-varying delay and sector-bounded nonlinearity using Lyapunov-Krasovskii (LK) functional approach. The proposed analysis, owing to the candidate LK functional and tighter bounding of its time-derivative, yields less conservative absolute and robust stability criteria for nominal and uncertain systems respectively. The effectiveness of the proposed criteria over some of the recently reported results is demonstrated using a numerical example.

Consensus in symmetric multi-agent networks with sector nonlinear couplings

AbstractWe investigate consensus dynamics in multi-agent networked systems with time-varying undirected topology and uncertain scalar-valued nonlinear couplings, satisfying sector inequalities. Using the Kalman-Yakubovich-Popov lemma and techniques of the absolute stability theory, we obtain consensus criteria for the networks of the specified type, analogous to the celebrated circle stability criterion for Lurie systems.