Class Of Lur Research Articles

Sampled-data synchronization of chaotic Lur’e systems via an adaptive event-triggered approach

In this paper, based on nonuniform sampling, the master-slave synchronization in a class of Lur’e systems is studied via using the sampled outputs of error system. Different from existing results, the transmission of control signals is determined by a novel adaptive event-triggered scheme, where the triggering thresholds depend on the dynamic behaviors of controlled systems rather than the predetermined constants as some traditional ones. Through choosing two augmented Lyapunov–Krasovskii functionals (LKFs), some delay-dependent synchronization criteria are formulated and the conservatism can be effectively reduced owing to the utilization of Wirtinger-based inequalities and delay-product-type LKF terms. Especially, the existence of the controller can be easily checked since the derived conditions are presented via LMI forms. Finally, two numerical examples with comparisons and simulations are given to illustrate the proposed results.

The converging-input converging-state property for Lur\u2019e systems

Using methods from classical absolute stability theory, combined with recent results on input-to-state stability (ISS) of Lur’e systems, we derive necessary and sufficient conditions for a class of Lur’e systems to have the converging-input converging-state (CICS) property. In particular, we provide sufficient conditions for CICS which are reminiscent of the complex Aizerman conjecture and the circle criterion and connections are also made with small gain ISS theorems. The penultimate section of the paper is devoted to non-negative Lur’e systems which arise naturally in, for example, ecological and biochemical applications: the main result in this context is a sufficient criterion for a so-called “quasi CICS” property for Lur’e systems which, when uncontrolled, admit two equilibria. The theory is illustrated with numerous examples.

High-gain fractional-order controller for output tracking and disturbance attenuation in a class of Lur'e systems

This paper addresses the problem of output tracking and attenuation of unknown disturbances acting on a class of nonlinear systems that consists of a forward path containing a linear, time-invariant element and a feedback path with a sector-bounded nonlinearity. Under the hypothesis that the frequency response of the linear block belongs to a half-plane, passing through the origin of the complex plane and forming an angle in [0,p/2] with the positive imaginary axis, a high-gain fractional-order controller is proposed to guarantee absolute stability of the nonlinear system. Numerical simulations demonstrate the properties of the method in a variety of conditions.

Improved robust stability criteria for a class of Lur'e systems with interval time-varying delays and sector-bounded nonlinearity

This paper is concerned with the absolute and robust stability for a class of neutral-type Lur'e systems with an interval time-varying delay and sector-bounded nonlinearity. By discretising the delay interval into two segmentations with an unequal width, new delay-dependent sufficient conditions for the absolute and robust stability of neutral-type Lur'e systems are proposed in terms of linear matrix inequalities (LMIs) by employing a modified Lyapunov-Krasovskii functional (LKF). These conditions reduce the conservativeness in computing the maximum allowed delay bounds (MADBs) in many cases. Finally, several standard numerical examples are presented to show the effectiveness of the proposed approach.

Dynamic output feedback stabilization for systems with sector-bounded nonlinearities and saturating actuators

In the present work a systematic methodology for computing dynamic output stabilizing feedback control laws for nonlinear systems subject to saturating inputs is presented. In particular, the class of Lur'e type nonlinear systems is considered. Based on absolute stability tools and a modified sector condition to take into account input saturation effects, an LMI framework is proposed to design the controller. Asymptotic as well as input-to-state and input-to-output (in a L2 sense) stabilization problems are addressed both in regional (local) and global contexts. The controller structure is composed of a linear part, an anti-windup loop and a term associated to the output of the dynamic nonlinearity. Convex optimization problems are proposed to compute the controller considering different optimization criteria. A numerical example illustrates the potentialities of the methodology.

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

Impulsive synchronization of chaotic Lur'e systems via partial states

In this Letter, the problem of impulsive synchronization of two identical Lur'e systems via partial states is studied. The problem arises in the situation when only partial states of the driven systems are available. By using the method of the variation of parameters for linear impulsive systems and some analysis technique, a sufficient condition for the existence of the impulsive control law for synchronization via partial states is derived. The sufficient condition is given in terms of linear matrix inequalities concerning the interconnection matrices. By using this result, we propose a new impulsive synchronization scheme for a class of Lur'e systems. The new impulsive synchronization scheme only exerts the impulsive input on partial states of the driven system and is characterized by a set of conditions related to the impulsive interval bound, the impulsive magnitude and a coupling condition between them. The proposed impulsive synchronization method is illustrated through Chua's circuit.

EXPERIMENTAL RESULTS ON CHUA'S CIRCUIT ROBUST SYNCHRONIZATION VIA LMIs

This paper investigates the synchronization of coupled chaotic systems using techniques from the theory of robust [Formula: see text] control based on Linear Matrix Inequalities. To deal with the synchronization of a class of Lur'e discrete time systems, a project methodology is proposed. A laboratory setup based on Chua's oscillator circuit is used to demonstrate the main ideas of the paper in the context of the problem of information transmission.

Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays

Abstract In this paper, we aim to study the robust global exponential synchronization problem for a general class of Lur’e chaotic systems subject to time delays and impulsive disturbances. Furthermore, we also provide an estimation of the maximum Lyapunov exponent. By using the Lyapunov function method and linear matrix inequality (LMI) technique, sufficient conditions for the robust global exponential synchronization and estimation of its maximum Lyapunov exponent are obtained for the class of Lur’e chaotic systems with and without time delays, respectively. Furthermore, by applying the M-matrix theory, some of these sufficient conditions are shown to be expressible in forms of fairly simple algebraic conditions. For illustration, several examples are solved by using the sufficient conditions obtained.

A NEW SYNCHRONIZATION PRINCIPLE FOR A CLASS OF LUR'E SYSTEMS WITH APPLICATIONS IN SECURE COMMUNICATION

In this Letter, we propose a new synchronization principle for a class of Lur'e systems. We design, using only a single scalar output, a possible class of observers to detect whether two dynamical systems exhibit identical oscillations. The proposed method is then applied to suggest a means to secure communications. The transmitter contains a chaotic oscillator with an input that is modulated by the information signal. The receiver is a copy of the transmitter driven by a synchronization signal. The advantage of this method over the existing one is that the synchronization time is explicitly computed. An illustrative example of the cubic Chua's circuit is given to show the effectiveness of the proposed approach.

ROBUST DEAD-BEAT SYNCHRONIZATION AND COMMUNICATION FOR DISCRETE-TIME CHAOTIC SYSTEMS

This paper proposes synchronization and chaotic communication for a class of Lur'e type discrete-time chaotic systems. The scalar outputs are suitably chosen in a flexible manner to be linear, nonlinear, or predictive, and along with the drive system are then written in an output injection form. Then with a suitable design of an observer-based response system, dead-beat performance is achieved for synchronization and chaotic communications. Then disturbances in the drive system are considered. Using an ℋ∞performance criterion, the disturbance is attenuated to a prescribed level by solving linear matrix inequalities (LMIs). Numerical simulations are carried out to verify the dead-beat performance.

Quasi-Jacobi Matrices, RC Networks and Aizerman's Conjecture

In this paper a connection is given for a class of quasi-Jacobi matrices, the class of RC impedance functions and Aizerman's Conjecture for nonlinear feedback systems. As results, realizability conditions for RC networks are established and a class of Lur'e type systems satisfying Aizerman's conjecture is characterized, Special quasi-Jacobi state-space realizations (tridiagonal (or Jacobi) and “arrow”) lead to algebraic tests for the verification of Aizerman's Conjecture.

Design of tunable digital set-point tracking and disturbance-rejection controllers for Lur'e plants with multiple non-linearities

Abstract The class of Lur'e plants with multiple non-linearities which are amenable to tunable error-actuated digital control ia characterized in terms of the properties of the transfer function matrices of the linear components of such plants. It is shown that this characterization greatly facilitates the design of closed-loop digital control systems incorporating such Lur'e plants which exhibit state-bounded absolutely stable tracking. These general results are illustrated by designing a tunable error-actuated digital set-point tracking and disturbance-rejection controller for a Lur'e plant in corporating a boiler furnace with four non-linear actuators.

High-Gain Tracking Systems Incorporating Lur'e Plants with Multiple Switching Nonlinearities

The class of Lur'e plants with multiple switching nonlinearities which are amenable to high-gain error-actuated control is characterised in terms of the properties of the transfer function matrices of the linear components of such plants. It is shown that this characterisation greatly facilitates the synthesis of closed-loop control systems incorporating such Lur'e plants which exhibit state-bounded absolutely stable tracking. These general results are illustrated by synthesizing a high-gain tracking system incorporating a Lur'e plant with two switching nonlinearities.

Fast-sampling tracking systems incorporating Lur'e plants with multiple non-linearities

The class of Lur'e plants with multiple non-linearities which are amenable to fast-sampling error-actuated digital control is characterized in terms of the properties of the transfer function matrices of the linear components of such plants. It is shown that. this characterization greatly facilitates the synthesis of closed-loop digital control systems incorporating such Lur'e plants which exhibit state-bounded absolutely stable tracking. These general results are illustrated by synthesizing a fast-sampling tracking system incorporating a Lur'e plant with two non-linearities.

High-gain tracking systems incorporating Lur'e plants with multiple non-linearities

The class of Lur'e plants with multiple non-linearities which are amenably to high-gain error-actuated control is characterized in terms of the properties of the transfer function matrices of the linear components of such plants. It is shown that this characterization greatly facilitates the synthesis of closed-loop control systems incorporating such Lur'e plants which exhibit state-bounded absolutely stable tracking. These general results are illustrated by synthesizing a high-gain tracking system incorporating a Lur'e plant with two non-linearities.