Sufficient and necessary conditions for absolute stability of time-delayed Lurie control systems

In this paper, we present some sufficient and necessary conditions for the absolute stability of time-delayed Lurie control systems, which improve the results we obtained before for the absolute stability of direct control, indirect control and critical control of Lurie systems. We also derived certain simple and easy applicable algebraic sufficient conditions for the absolute stability of time-delayed Lurie control systems, which provide a convenient tool for practical control engineers in designing absolutely stable systems or stabilizing nonlinear control systems.     

一类中立型间接控制系统的鲁棒绝对稳定性

研究了有多个执行机构的多滞后中立型间接不确定Lurie控制系统的鲁棒绝对稳定性,借助于Lyapunov泛函构造方法,给出了关于Lyapunov泛函中正定矩阵和积分项参数的线性矩阵不等式(LMI)的稳定性判别准则,且与时滞量的大小无关.最后举例说明了本文结果的有效性.     

Improved delay-dependent robust stability criteria for uncertain time delay systems

This paper deals with the robust stability analysis for uncertain systems with time-varying delay. New delay-dependent robust stability criteria of uncertain time-delay systems are proposed by exploiting appropriate Lyapunov functional candidate. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism, due to the introduction of a method to estimate the upper bound of the derivative of Lyapunov functional candidate without ignoring the additional useful terms. Numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method.     

具有滞后型执行机构的Lurie控制系统的绝对稳定性

本对于具有滞后型执行机构的Lurie控制系统，构造了一个关于Liqpunov泛函中自由参数的LMI，通过这个LMI的解来构造Liapunov泛函保证系统了的绝对稳定性，最后给出实例说明本方法的有效性。     

多时滞退化Lurie控制系统的绝对稳定性

本文研究退化Lurie直接控制时滞系统和退化Lurie间接控制时滞系统的绝对稳定性,基于Lyapunov稳定性理论和线性矩阵不等式得到绝对稳定的判据,即绝对稳定性仅仅依赖于时滞导数的大小.特别地,时滞可以是无界的函数,仿真示例同时说明了此方法的有效性.     

Absolute stability criteria for a class of nonlinear singular systems with time delay

This paper deals with the problem of absolute stability for a class of time-delay singular systems with sector-bounded nonlinearity. Both delay-independent and delay-dependent criteria are presented and formulated in the form of linear matrix inequalities (LMIs). Neither model transformation nor a bounding technique for cross-terms, nor a slack variable method is involved in obtaining the stability criteria. Numerical examples are given to show the effectiveness and improvements over some existing results.     

Robust exponential stability and stabilizability of linear parameter dependent systems with delays

The robust exponential stability and stabilizability problems are addressed in this paper for a class of linear parameter dependent systems with interval time-varying and constant delays. In this paper, restrictions on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive delay-dependent exponential stability and stabilizability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to illustrate the effectiveness of our theoretical results.     

Improved delay-dependent stability criterion for neural networks with time-varying delay

In this paper, the problem of delay-dependent asymptotic stability criterion for neural networks with time-varying delay has been considered. A new class of Lyapunov functional which contains a triple-integral term is constructed to derive some new delay-dependent stability criteria. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Application of semi-definite programming to robust stability of delay systems

We study here robust stability of linear systems with several uncertain incommensurate delays, more precisely the property usually called delay-dependent stability. The main result of this paper consists in establishing that the latter is equivalent to the feasibility of some Linear Matrix Inequality (LMI), a convex optimization problem whose numerical solution is well documented.The method is based on two main techniques:

• use of Padé approximation to transform the system into some singularly perturbed finite-dimensional system, for which robust dichotomy has to be checked;

• recursive applications of Generalized Kalman–Yakubovich–Popov (KYP) lemma to characterise by an LMI the previous property.

Stochastic stability and robust control for sampled-data systems with Markovian jump parameters

In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.     

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

具多个非线性反馈项的一般Lurie控制系统的绝对稳定性

本文研究了具多个非线性反馈项的一般Lurie控制系统的绝对稳定性问题,由Lyapunov函数方法,得出了绝对稳定的新的充分必要条件和一些实用的充分条件,这些条件推广了集合稳定性.一个数值例子说明了本文结果的有效性.     

Absolute Stability of General Lurie Control Systems with Multi-Nonlinear Feedback Terms

In this paper, the problem of absolute stability for general Lurie control systems with multi-nonlinear feedback terms is investigated. From the Lyapunov function approach, new necessary and sufficient conditions and some practical sufficient conditions of absolute stability are derived, which improve the absolute stability for the set. A numerical example illustrates the effectiveness of the proposed results. The project is supported by the National Natural Science Foundation of China (No. 19871005) and the Foundation of Doctoral Programme of the Educational Ministry of China (No. 1999000722)     

Non-fragile observer-based passive control for uncertain time delay systems subjected to input nonlinearity

The problem of non-fragile observer-based passive control for uncertain time delay systems subjected to input nonlinearity is investigated by using sliding mode control. A novel control law is established such that the sliding surface in the state-estimation space can be reached in a finite time and chattering reduction is obtained. A sufficient condition for passivity and asymptotic stability of the combined system is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantages of the proposed method.     

Global asymptotic stability for a class of nonlinear neural networks with multiple delays

This paper investigates the global asymptotic stability (GAS) for a class of nonlinear neural networks with multiple delays. Based on Lyapunov stability theory and the linear matrix inequality (LMI) technique, a less conservative delay-dependent stability criterion is derived. The present result is shown to be less conservative than those given in the literature.     

Robust stability analysis of uncertain systems with two additive time-varying delay components

This paper is concerned with stability analysis for uncertain systems. The systems are based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components and parameter uncertainties. Numerical examples show that the proposed criteria are effective and are an improvement over some existing results in the literature.     

Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach

This paper is concerned with the problem of asymptotic stability of neutral systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality to ensure a large upper bound of the time-delay by non-uniformly dividing the delay interval into multiple segments. A new Lyapunov-Krasovskii functional is constructed with different weighting matrices corresponding to different segments in the Lyapunov-Krasovskii functional, where both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Strongly absolute stability of Lur'e type differential-algebraic systems

In this paper, we consider Lur'e type differential-algebraic systems (LDS) and introduce the concept of strongly absolute stability. Such a notion is a generalization of absolute stability for Lur'e type standard state-space systems (LSS). By a Lur'e type Lyapunov function, we derive an LMI based stability criterion for LDS to be strongly absolutely stable. Using extended strictly positive realness (ESPR), we present the frequency-domain interpretation of the obtained criterion, by which we simplify the criterion and show that the criterion is a generalization of the well-known Popov criterion. Finally, we illustrate the effectiveness of the main results by a numerical example.