Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

A New Criterion for Stability of Large-Scale Systems with Delay

A simple criterion for delay-independent stability of large-scale linear time-varying systems is deduced by employing a type of Lyapunov function. The notable features of the results in this paper are its simplicity and efficiency in testing the stability large-scale linear time-varying systems. Some illustrative examples are given to demonstrate the advantages of the obtained results over those in literature.

Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems

In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.

A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular model, called Forna- sini-Marchesini (FM) second model was proposed by Fornasini and Marchesini in 1978. The aim of this paper is to present a survey of the existing literature on the stability of FM second model.

Integralinput-to-statestability ystemswithsmalldelays Integral input-to-state stability of systems with small delays

We consider how small delays affect the integral-input-to-state stability(iss)property for a system.Our result is similar to the input-to-state stability(Iss)result obtained in[1]:the iss property will be preserved in a practical and semi-global manner if the delay interval is small enough.However,since the iss quantifies the robust stability in terms of a generalized Li norm of the inputs instead of a generalized Loo norm of the inputs for the Iss case,the techniques and proofs for the Iss case do not apply to the iss case directly.While the proofs in[1]are based on the Lyapunov-Razumikhin approach,our proofs are based on the iss-Lyapunov functions for the zero-delay system.In addition to the interest by its own in showing how the iss property is affected by small delays,the result also serves to the study of the iss property for singularly perturbed systems.

Lyapunov Stability Analysis for Incommensurate Nabla Fractional Order Systems

This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems.In particular,both Caputo definition and Riemann-Liouville definition are under consideration.With the convex assumption,several elementary fractional difference inequalities on Lyapunov functions are developed.According to the essential features of nabla fractional calculus,the sufficient conditions are given first to guarantee the asymptotic stability for the incommensurate system by using the direct Lyapunov method.To substantiate the efficacy and effectiveness of the theoretical results,four examples are elaborated.

Robust Stability of Neutral Systems:A Discretized Lyapunov Functional Method

This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method.

The Variational Lyapunov Method and Stability for Impulsive Delay Differential Systems

By using the variational Lyapunov method and Razumikhin technique, the stability criteria in terms of two measures for impulsive delay differential systems are established. The known results are generalized and improved. An example is worked out to illustrate the advantages of the theorems.

Stability and boundedness in terms of two measures for nonlinear impulsive control systems

In this paper we study stability and boundedness in terms of two measures for impulsive control systems. By using variational Lyapunov method, a new variational comparison principle and some criteria on stability and boundedness are obtained. An example is presented to illustrate the efficiency of proposed result.

Stability of Nonlinear Differential-Algebraic Systems Via Additive Identity

The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Direct Method. In addition, a novel interpretation of differential-algebraic systems as feedback interconnection of a purely differential system and an algebraic system allows reducing the stability analysis to a smallgain-like condition. The study of stability properties for constrained mechanical systems, for a class of Lipschitz differential-algebraic systems and for an academic example is used to illustrate the theory.

Stability Criteria for Large－Scale Linear Systems with Structured Uncertainties

The robust stability analysis for large scale linear systems with structured time varying uncertainties is investigated in this paper.By using the scalar Lyapunov functions and the properties of M matrix and nonnegative matrix,stability robustness measures are proposed.The robust stability criteria obtained are applied to derive an algebric criterion which is expressed directly in terms of plant parameters and is shown to be less conservative than the existing ones.A numerical example is given to demonstrate the stability criteria obtained and to compare them with the previous ones.

THE STABILITY ANALYSIS ON MODEL FOL LOWING LSS AND THE TIME-VARYING WEIGHTED SUM METHOD

The previous stability problem of large-scale systems(LSS) is mainly the stability of the null solution X=0 of the composite system(CS) described

Adaptive Robust Control for A Class of Nonlinear Systems with Unknown Uncertainties

The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.

GLOBAL EXPONENTIAL STABILITY FOR AN IMPULSIVE DELAYED INTEGRO-DIFFERENTIAL EQUATION

In this paper, the stability of an impulsive integro-differential equation with finite and infinite delays is investigated. By applying the Lyapunov-Razumikin method, sufficient condition for global exponential stability of such equation is obtained.

State Feedback Control for a Class of Fractional Order Nonlinear Systems

Using the Lyapunov function method, this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form, and presents a number of new results. First, some new properties of Caputo fractional derivative are presented, and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties. Then, by introducing appropriate transformations of coordinates, the problem of controller design is converted into the problem of finding some parameters, which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. © 2014 Chinese Association of Automation.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

DoS攻击下抛物型多智能体系统的输出反馈领导-跟随一致性

为了解决抛物型多智能体系统(MASs)在拒绝服务(DoS)攻击下的一致性问题,提出了一种基于输出反馈方法的MASs领导-跟随一致性控制协议来应对恶意攻击者发起的DoS攻击,从而实现智能体在无向通信拓扑图上的领导-跟随一致性。对DoS攻击的频率和持续时间进行了分析,利用Lyapunov稳定性定理推导了抛物型偏微分系统的稳定条件,证明了触发时间间隔不为零,避免了芝诺行为的发生,并通过仿真算例验证了理论结果的有效性。

单相并网储能双向变流器线性时间周期模型的稳定性分析

针对传统线性时不变模型无法描述储能双向变流器多频次谐波间交互耦合现象的问题,提出了一种单相并网储能双向变流器的线性时间周期模型,并进行稳定性分析。基于线性时间周期理论对单相并网储能双向变流器进行建模,得到非线性时间周期模型;围绕周期轨道将该模型线性化,得到储能双向变流器的线性时间周期时域模型;通过傅里叶展开推出了储能双向变流器的线性时间周期频域模型;利用李雅普诺夫第一方法分析比例积分控制器在不同参数下的储能双向变流器小信号模型的稳定性及稳定边界。MATLAB/Simulink仿真实验结果表明:建立的单相并网储能双向变流器的线性时间周期模型具有准确性和稳定性,稳定性边界正确。

广义系统渐近稳定分析与镇定的Lyapunov方法

利用Lyapunov方法研究了广义系统的渐近稳定性分析及控制问题,首先提出一种新形式的Lyapunov方程,用来研究广义系统渐近稳定性与镇定问题,同时给出了利用Lyapunov方程判定具有脉冲形式下广义系统渐近稳定的充分必要条件。利用相应的Riccati方程完成镇定广义系统的状态反馈控制器的设计。本文所有结论对广义系统有无脉冲行为均适用。最后利用数值例子说明主要结果。