Stability Of Lur Research Articles

Exponential input-to-state stability for Lur’e systems via Integral Quadratic Constraints and Zames–Falb multipliers

Abstract Absolute stability criteria that are sufficient for global exponential stability are shown, under a Lipschitz assumption, to be sufficient for the a priori stronger exponential input-to-state stability property. Important corollaries of this result are as follows: (i) absolute stability results obtained using Zames–Falb multipliers for systems containing slope-restricted nonlinearities provide exponential input-to-state-stability under a mild detectability assumption; and (ii) more generally, many absolute stability results obtained via Integral Quadratic Constraint methods provide, with the additional Lipschitz assumption, this stronger property.

Incremental input-to-state stability for Lur'e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing

We prove (integral) input-to-state stability results for a class of forced Lur'e differential inclusions and use them to investigate incremental (integral) input-to-state stability properties of Lur'e differential equations. The latter provide a basis for the derivation of convergence results for trajectories of Lur'e equations generated by Stepanov almost periodic inputs.

On Delay-dependent and Delay-derivative-dependent Stability and Stabilization for Lur’e Systems with Slow-varying Delay

This note is concerned with the absolute stability for time-varying delay Lur’e system with sector-bounded nonlinearity. Improved delay-dependent and delay-derivative-dependent stability criteria are obtained in the form of linear matrix inequalities (LMIs) by constructing a modified augmented Lyapunov-Krasovskii (LK) functional without applying the model transformation or the bounding techniques for cross terms. Thus, the presented delay-dependent criteria are less conservative than those in the literature. Moreover, state feedback stabilizing controllers based on the proposed stability criteria are designed. Numerical example demonstrates the effectiveness and superiority of the proposed method.

New Absolute Stability Conditions of Lur’e Systems with Time-Varying Delay

This paper is focused on the absolute stability of Lur’e systems with time-varying delay. Based on the quadratic separation framework, a complete delay-decomposing Lyapunov-Krasovskii functional is constructed. By considering the relationship between the time-varying delay and its varying interval, improved delay-dependent absolute stability conditions in terms of linear matrix inequalities (LMIs) are obtained. Moreover, the derived conditions are extended to systems with time-varying structured uncertainties. Finally, a numerical example is given to show the advantage over existing literatures.

Robust stability analysis for Lur’e systems with interval time-varying delays via Wirtinger-based inequality

Abstract This paper considers the problem of robust stability for Lur’e systems with interval time-varying delays and parameter uncertainties. It is assumed that the parameter uncertainties are norm bounded. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative sufficient stability conditions of the concerned systems are introduced within the framework of linear matrix inequalities (LMIs). Three numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

On computing maximum allowable time delay of Lur’e systems with uncertain time-invariant delays

In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix eliminating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.

Input-to-State Stability of Lur’e Hyperbolic Distributed Complex-Valued Parameter Control Systems: LOI Approach

In this work, input-to-state stability of Lur’e hyperbolic distributedcomplex-valuedparameter control systems has been addressed. Using comparison principle, delay-dependent sufficient conditions for the input-to-state stability in complex Hilbert spaces are established in terms of linear operator inequalities. Finally, numerical computation illustrates our result.

Stabilization of Lur’e-type nonlinear control systems by Lyapunov-Krasovskii functionals

Abstract The paper deals with the stabilization problem of Lur’e-type nonlinear indirect control systems with time-delay argument. The sufficient conditions for absolute stability of the control system are established in the form of matrix algebraic inequalities and are obtained by the direct Lyapunov method. MSC:34H15, 34K20, 93C10, 93D05.

Improved delay-dependent absolute stability of Lur’e systems with time-delay

The problem of absolute stability of Lur’e systems with time-delay is investigated in this paper. By employing a new Lyapunov-Krasovskii functional with the idea of N-segmentation of delay length, less conservative delay-dependent stability criteria are obtained and formulated in the form of linear matrix inequalities (LMIs). Numerical example shows that the results obtained in this paper are better than existing ones.

Improved delay-dependent absolute stability and robust stability for a class of nonlinear systems with a time-varying delay

This paper investigates the problem of the absolute stability of Lur'e systems with a time-varying delay. By considering the relationships among the time-varying delay, its upper bound, and the difference between them, less conservative delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities, without ignoring any useful terms in the derivative of a Lyapunov–Krasovskii functional. Numerical example shows that the results obtained in this paper are better than the previous results. Copyright © 2009 John Wiley & Sons, Ltd.

Frequency-domain and time-domain methods for feedback nonlinear systems and applications to chaos control

This paper surveys frequency-domain and time-domain methods for feedback nonlinear systems and their possible applications to chaos control, coupled systems and complex dynamical networks. The absolute stability of Lur’e systems with single equilibrium and global properties of a class of pendulum-like systems with multi-equilibria are discussed. Time-domain and frequency-domain criteria for the convergence of solutions are presented. Some latest results on analysis and control of nonlinear systems with multiple equilibria and applications to chaos control are reviewed. Finally, new chaotic oscillating phenomena are shown in a pendulum-like system and a new nonlinear system with an attraction/repulsion function.

On Absolute Stability of Lur’e Control Systems with Multiple Non-Linearities

This paper presents necessary and sufficient conditions for the existence of a Lyapunov function in the Lur’e form that guarantees the absolute stability of a Lur’e control system with multiple nonlinearities. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If these inequalities are feasible,the free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms,are given by the solution of the LMIs. Otherwise,there does not exist any Lyapunov function in the Lur’e form. Necessary and sufficient conditions are also obtained for the robust absolute stability of time-varying structured uncertain systems.

On absolute stability of Lur’e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur ’ e form to guarantee the absolute stability of Lur’ e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.

一般的なセクタ型非線形要素と区間プラントを含むルーリエ系のロバスト絶対安定性

一般的なセクタ型非線形要素と区間プラントを含むルーリエ系のロバスト絶対安定性