Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.

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.

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

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.

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.

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.

The Sufficient Conditions for Robust Absolute Stability of Lurie Control Systems

In this paper, the problem of absolute stability of continuous time with parametric nonlinear system uncertainty of a linear part and sector uncertainty of its nonlinear part is considered, the and sufficient conditions for absolute stability of direct and indirect control systems are presented. The corresponding results for robust absolute stability are improved.

Reliability and sensitivity analysis of loop-designed security and stability control system in interconnected power systems

Security and stability control system(SSCS)in power systems involves collecting information and sending the decision from/to control stations at different layers;the tree structure of the SSCS requires more levels.Failure of a station or channel can cause all the execution stations(EXs)to be out of control.The randomness of the controllable capacity of the EXs increases the difficulty of the reliability evaluation of the SSCS.In this study,the loop designed SSCS and reliability analysis are examined for the interconnected systems.The uncertainty analysis of the controllable capacity based on the evidence theory for the SSCS is proposed.The bidirectional and loop channels are introduced to reduce the layers and stations of the existing SSCS with tree configuration.The reliability evaluation and sensitivity analysis are proposed to quantify the controllability and vulnerable components for the SSCS in different configurations.By aiming at the randomness of the controllable capacity of the EXs,the uncertainty analysis of the controllable capacity of the SSCS based on the evidence theory is proposed to quantify the probability of the SSCS for balancing the active power deficiency of the grid.

Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

Delay-dependent robust stability of uncertain networked control systems with multiple state time-delays

In this paper, delay-dependent robust stability for a class of uncertain networked control systems （NCSs） with multiple state time-delays is investigated. Modeling of multi-input and multi-output （MIMO） NCSs with networkinduced delays and uncertainties through new methods are proposed. Some new stability criteria in terms of LMIs are derived by using Lyapunov stability theory combined with linear matrix inequalities （LMIs） techniques. We analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound （MADB） for the NCSs with the proposed methods. Compared with the reported results, the proposed results obtain a much less conservative MADB which are more general. Numerical example and simulation is used to illustrate the effectiveness of the proposed methods.

ABSOLUTE STABILITY OF CONTROL SYSTEM WITH MULTI-NONLINEAR FEEDBACK TERMS

In this paper, the absolute stability of control systems with multi nonlinear feedback terms are studied. The sufficient and necessary conditions of absolute stability are obtained. Some applied sufficient conditions of absolute stability are given.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

New Delay-dependent Absolute Stability Criteria for Lurie Control Systems

这笔记为时间延期 Lurie 控制系统涉及绝对稳定性分析，非线性在一个无限的扇区和有限扇区定位了。由使用新 Lyapunov-Krasovskii 功能那把整个延期间隔切成二个子区间并且在每个子区间和介绍一些上定义不同精力功能免费重量的矩阵，某新延期依赖者要用体力地绝对的稳定性标准以严格的线性矩阵不平等(LMI ) 被介绍。获得的延期依赖者标准不比以前的保守，作为被数字例子说明。

Impulsive control of permanent magnet synchronous motors with parameters uncertainties

The permanent magnet synchronous motors （PMSMs） may have chaotic behaviours for the uncertain values of parameters or under certain working conditions, which threatens the secure and stable operation of motor-driven. It is important to study methods of controlling or suppressing chaos in PMSMs. In this paper, robust stabilities of PMSM with parameter uncertainties are investigated. After the uncertain matrices which represent the variable system parameters are formulated through matrix analysis, a novel asymptotical stability criterion is established. Some illustrated examples are also given to show the effectiveness of the obtained results.

Robustness Analysis of Discrete-time Indirect Model Reference Adaptive Control with Normalized Adaptive Laws

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control （MRAC） with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter are also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.

On delay-dependent robust stability for uncertain neutral systems

The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some free-weighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.

Stability analysis of time-varying systems via parameter-dependent homogeneous Lyapunov functions

This paper considers the stability analysis of linear continuous-time systems, and that the dynamic matrices are affected by uncertain time-varying parameters, which are assumed to be bounded, continuously differentiable, with bounded rates of variation. First, sufficient conditions of stability for time-varying systems are given by the commonly used parameter-dependent quadratic Lyapunov function. Moreover, the use of homogeneous polynomial Lyapunov functions for the stability analysis of the linear system subject to the time-varying parametric uncertainty is introduced. Sufficient conditions to determine the sought after Lyapunov function is derived via a suitable paramenterization of polynomial homogeneous forms. A numerical example is given to illustrate that the stability conditions are less conservative than similar tests in the literature.

New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Descriptor Systems

The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.