Stability and passivity analysis for Lur’e singular systems with Markovian switching

This paper is concerned with the stochastic stability and passivity analysis for a class of Lur’e singular systems with time-varying delay and Markovian switching. By using the free-weighting matrices approach, a delay-dependent stability criterion, which guarantees that the system is stochastically stable and robustly passive, is derived in terms of linear matrix inequality (LMI). Two numerical examples are provided to illustrate the effectiveness of the proposed method.     

Impulsive control of Lur’e systems

This paper presents an impulsive control scheme of the Lur’e system. We provide several sufficient conditions for the stabilization and synchronization of Lur’e systems via impulsive control with varying impulsive intervals. The efficiency of the result is illustrated through a numerical example.     

Master-slave synchronization of singular Lur’e systems with time-delay

This paper is concerned with the problem of designing a time-delay output feedback control law for master-slave synchronization of singular Lur’e systems. Using generalized Lyapunov stability theory, a sufficient condition for the existence of such feedback control law is given and an explicit expression of such control law is also achieved. These algorithms are formulated in terms of linear matrix inequalities, which can be easily performed numerically. A numerical example is used to illustrate the effectiveness of the design method.     

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.     

Synchronization of general discrete Lur＇e systems

This paper studies a master-slave type of synchronization systems for a general form of two discrete Lur＇e systems. Some simple necessary and/or sufficient conditions for synchronization are derived. They are basically algebraic conditions, and are convement to be applied in engineering applications.     

Improved Sufficient LMI Conditions for the Robust Stability of Time-delayed Neutral-type Lur’e Systems

International Journal of Control, Automation and Systems - In this paper, we focus on the problem of the absolute and robustly absolute stability for the neutral-type Lur’e system with...     

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.     

Constrained controllability of discrete-time systems†

The constrained controllability of the discrete-time system x_k+1=A(k)x_k+B(k)u,_k is considered where the control uk is termed admissible if it satisfies specified magnitude constraints. Constrained controllability is concerned with the existence of an admissible control which steers the state x to a given target set from a specified initial state

Conditions for checking constrained controllability to a given target set from a specified initial state are presented. These conditions involve solving finite-dimensional optimization problems and can be checked via numerical computation. In addition, conditions for checking global constrained controllability to a given target set are presented. A system is globally constrained controllable if for every initial state, there exists an admissible control that steers the system to the target.

If a given discrete-time system is constrained controllable, it may be desirable to obtain an admissible control that steers the system to the target from a specified initial state. Such a control is called a steering control. Results for computing steering controls are also presented

This paper is concluded with a numerical example. In this example, it is shown that the constrained controllability of a continuous-time system which has been discretized is dependent on the discretization time. The set of states which can be steered to the target changes as the discretization time changes. Furthermore, the example shows that a discrete-time steering control cannot always be obtained by discretizing a continuous-time steering control; the steering control for the discrete-time system must be obtained directly from the discrete-time model.     

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

     

Satisfactory control of discrete-time linear periodic systems

In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that desired requirements of steady state covariance, H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously. By using satisfactory control theory, the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities （LMIs）, and a feasible designing approach is presented via LMI technique. Numeric example validates the obtained conclusion.     

Conjugation and H ∞ control of discrete-time systems

We establish conjugation notion in discrete-time systems, first introduced into the H ^∞ control theory of continuous-time systems by Kimura (1989). In discrete-time systems, conjugation is a very elementary operation on rational transfer functions that replaces some of their poles by their reflections with respect to the unit circle. With the aid of J-lossless conjugation conjugation by a J.lossless system), it is shown that the parametrization of sub-optimal solutions of H ^∞ model-matching problems is reduced to a Lyapunov-type equation. The parametrization of all solutions is given in an extremely simple way. It is further proved that the J-lossless conjugation of the H ^∞ model-matching problem is a natural state-space representation of classical interpolation in discrete-time systems.     

Some new criteria for lag synchronization of chaotic Lur＇e systems by replacing variables control

Some new criteria for the chaotic lag synchromzation are proposed. At first, lag synchronization scheme for identical master-slave Lur‘e systems by replacing variables control and the relevant error system are given, and the relations between absolute stability of the error system and the chaotic lag synchromzation are described. Then. based on a quadratic Lyapunov function, two new Lur‘e criteria for the above chaotic lag synchronization are proved. Four corresponding frequency domain criteria are further derived by means of Meyer-Kalman-Yacubovia Lemma. These frequency domain criteria are apphed to analyze the lag synchromzation of general master-slave Chua‘s circuits so that some ranges of the parameters in which the master-slave Chua‘s circuits achieve chaotic lag synchronization by replacing single-variable control are attained. Finally, some examples are given to verify the theoretical results.     

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 Lyaptmov 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.     

Stability of switched nonlinear systems via extensions of LaSalle’s invariance principle

This paper studies the extension of LaSalle’s invariance principle for switched nonlinear systems. Un-like most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle’s invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.     

Stability analysis of a class of non-linear distributed parameter systems—tubular chemical reactors†

A sufficient condition for local stability of the spatially discretized model of a class of non-linear distributed parameter systems is derived using the circle criterion for stability and bounded-input, bounded-output stability. As a physical system the catalytic packed-bed tubular reactor is taken to illustrate the application of the theorem to process control systems. The stability condition in the large derived from non-linear system equations is compared with the stability condition in the small derived from linearized system equations. Interpretations of the result are given in terms of physical variables.     

Error-based adaptive optimal tracking control of nonlinear discrete-time systems

In this paper,for the output tracking problem of nonlinear discrete-time systems,a performance index is newly defined using the adaptive dynamic programming(ADP) technique to completely eliminate tracking errors in theory.In contrast to traditional definitions of performance indices in other ADP-based methods,the proposed performance index is not only designed from the perspective of output tracking errors but also introduced errors of system states and control inputs at adjacent stages,which is...     

离散时滞Lur’e系统时滞依赖性稳定性判据

本文研究了离散时滞Lur’e系统的绝对稳定性和鲁棒绝对稳定性问题,包含时变时滞和扇形有界约束的非线性.首先,构造了新颖的李雅普诺夫-克拉索夫斯基泛函(Lyapunov-Krasovskii functional, LKF),其中,为了增补时变时滞区间和其他系统状态变量之间的耦合信息, LKF中扩充了一些重要的向量.其次,结合改进的基于自由权重矩阵求和不等式技巧,推导了一些比已有结论保守性更低的绝对和鲁棒绝对稳定性判据.稳定性判据保守性的减小主要归功于改进的LKF和求和不等式技巧.最后,通过几个文献中常用的数值算例的求解仿真来说明本文判据的有效性和先进性.