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 conditi...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.展开更多
The robust absolute stability of general Lurie interval direct control system with multiple nonlinearities, with respect to model variations, is considered. Some sufficient conditions of absolute stability for the sys...The robust absolute stability of general Lurie interval direct control system with multiple nonlinearities, with respect to model variations, is considered. Some sufficient conditions of absolute stability for the system are obtained, which generalize and improve the previous results.展开更多
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...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.展开更多
Definition 1. If （?）A∈A<sub>I</sub>, the zero solution of（1.2 ）is absolutely stable, then we say the interval system （1.1）is Robust absolutely stable, which is denoted by （1.1）∈RAS. Definition 2....Definition 1. If （?）A∈A<sub>I</sub>, the zero solution of（1.2 ）is absolutely stable, then we say the interval system （1.1）is Robust absolutely stable, which is denoted by （1.1）∈RAS. Definition 2. If （?）A∈A<sub>I</sub>, the zero solution of （1.2） is absolutely stable for partial variables x<sub>j0</sub>, …, x<sub>n+1</sub>, then we call the interval system （1.1）Robust absolutely stable for partial variables x<sub>j0</sub>, …, x<sub>n+1</sub>, which is denoted by （1.1）∈RAS （j0→n+1）.展开更多
考虑了关于模型变化的具有多非线性的区间 L urie控制系统的鲁棒绝对稳定性 .用 Lyapunov函数方法和区间分析技术 ,得到了区间 L urie系统鲁棒绝对稳定的一些充分条件 ,这些条件减少了绝对稳定鲁棒检测的保守性 .这些鲁棒分析方法是基...考虑了关于模型变化的具有多非线性的区间 L urie控制系统的鲁棒绝对稳定性 .用 Lyapunov函数方法和区间分析技术 ,得到了区间 L urie系统鲁棒绝对稳定的一些充分条件 ,这些条件减少了绝对稳定鲁棒检测的保守性 .这些鲁棒分析方法是基于区间矩阵的鲁棒稳定分析 .展开更多
文摘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.
文摘The robust absolute stability of general Lurie interval direct control system with multiple nonlinearities, with respect to model variations, is considered. Some sufficient conditions of absolute stability for the system are obtained, which generalize and improve the previous results.
基金This work was supported by the Doctor Subject Foundation of China (No. 2000053303)
文摘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.
基金Project supported by the National Natural Science Foundation of China
文摘Definition 1. If （?）A∈A<sub>I</sub>, the zero solution of（1.2 ）is absolutely stable, then we say the interval system （1.1）is Robust absolutely stable, which is denoted by （1.1）∈RAS. Definition 2. If （?）A∈A<sub>I</sub>, the zero solution of （1.2） is absolutely stable for partial variables x<sub>j0</sub>, …, x<sub>n+1</sub>, then we call the interval system （1.1）Robust absolutely stable for partial variables x<sub>j0</sub>, …, x<sub>n+1</sub>, which is denoted by （1.1）∈RAS （j0→n+1）.
