切换中立型系统稳定性分析
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摘要
本论文主要分析了切换中立型系统的稳定性,并对一些相关问题进行了深入讨论,得到了一些比较重要的结果。全文主要讨论了五个方面的问题:
一、应用Lyapunov泛函方法结合矩阵不等式技巧及自由权重矩阵思想,研究了同时含分布时滞和离散时滞的中立型系统的时滞依赖稳定性,得到了保守性较小的结果;通过使用时滞分解的方法,研究了带混合时滞和同时含离散时滞与分布时滞的中立型系统的稳定性,在引入新的Lyapunov泛函的基础上,进一步结合自由权重矩阵思想和矩阵不等式技巧,得到了保守性更小的稳定性结论。通过数值实例验证了所得结论的有效性。
二、分别采用Lyapunov泛函方法结合自由权重矩阵思想和等价系统方法研究了带离散时滞的常时滞切换中立型系统在一定切换规则下的稳定性,得到了相应的时滞依赖稳定性结论;用Lyapunov泛函方法结合自由权重矩阵思想研究了带离散时滞的常时滞切换中立型系统的稳定性和L2增益,得到了基于平均驻留时间的时滞依赖指数稳定充分条件及L2增益条件;采用Lyapunov泛函方法结合自由权重矩阵思想研究了带离散时滞和分布时滞的常时滞切换中立型系统在一定切换规则下的稳定性,得到了系统的时滞依赖稳定性充分条件。
三、用Lyapunov泛函方法结合自由权重矩阵思想研究了含时变离散时滞的切换中立型系统的稳定性,得到了基于平均驻留时间的指数稳定充分条件;用Lyapunov泛函方法研究了含非线性扰动的变时滞切换中立型系统的稳定性,得到了基于平均驻留时间的指数稳定性条件。
四、分别用Lyapunov泛函方法和Lyapunov函数结合Razumikhin方法研究了切换非线性中立型系统的稳定性,得到了系统稳定的充分条件。
五、用Lyapunov泛函方法研究了脉冲切换中立型系统的稳定性,得到了系统稳定的矩阵不等式条件。
本文所得到的系统稳定性条件大多是以线性矩阵不等式表示的,可以直接在Matlab下的LMI工具箱实现。
Addressed in this dissertation is the stability analysis of switched neutral systems. Several relevant problems are discussed in detail,and a series of important results are obtained. As a whole, this dissertation is consisted of the following five aspects.
Firstly, by using the method of Lyapunov-Krasovskii functionals combining the technique of matrix inequalities and theory of weighted matrices, the delay-dependent stability of neutral systems with distributed- and discrete-delays is studied, and some less conservative results are obtained; by decomposing time delays, the stability of neutral systems with mixed delays and neutral systems with distributed- and discrete-delays is studied, based on a new class of Lyapunov-Krasovskii functionals introduced in this dissertation, combining the technique of matrix inequalities and theory of weighted matrices,some much less conservative results are obtained. The examples are supplied to illustrate the effectiveness of the results presented in this chapter.
Secondly, by applying the method of Lyapunov-Krasovskii functionals, combining the idea of weighted matrix and the method of equivalent system, the stability under some switched rules of a class of switched neutral system with discrete time-delay is studied, and some stability criteria are obtained; the stability and L2-gain of a class of switched neutral system with discrete delay are studied, and some sufficient conditions for exponential stability and L2-gain stability are acquired based on average dwell time; by applying the method of Lyapunov-Krasovskii functionals, combining the idea of weighted matrix,the stability under some switched rules of a class of switched neutral system with discrete and distributed-delays is studied, and some delay-dependent stability criteria under some switched rules are obtained.
Thirdly, by applying the method of Lyapunov-Krasovskii functionals, combining the idea of weighted matrix, the stability of a class of switched neutral system with timevarying discrete delayis studied, and some sufficient conditions of exponential stability are reached based on average dwell time; by applying the method of Lyapunov-Krasovskii functionals, the stability of a class of switched neutral system with time-varying delay and nonlinear perturbation is studied, and some exponential stability conditions are obtained based on average dwell time.
Fourthly, the methods of Lyapunov-Krasovskii functionals and Lyapunov-Krasovskii functions combining Razumikhinthe method are used to study the stability of a class of switched nonlinear neutral systems, and some sufficient conditions of stability are obtained.
Finally, the method of Lyapunov-Krasovskii functionals is used to study the stability of a class of impulsive switched neutral systems, and some stability criteria are obtained in term of matrix inequalities.
All the stability criteria are expressed in terms of linear matrix inequalities(LMIs), and they can realized in Matlab using the kit of LMIs.
一、应用Lyapunov泛函方法结合矩阵不等式技巧及自由权重矩阵思想,研究了同时含分布时滞和离散时滞的中立型系统的时滞依赖稳定性,得到了保守性较小的结果;通过使用时滞分解的方法,研究了带混合时滞和同时含离散时滞与分布时滞的中立型系统的稳定性,在引入新的Lyapunov泛函的基础上,进一步结合自由权重矩阵思想和矩阵不等式技巧,得到了保守性更小的稳定性结论。通过数值实例验证了所得结论的有效性。
二、分别采用Lyapunov泛函方法结合自由权重矩阵思想和等价系统方法研究了带离散时滞的常时滞切换中立型系统在一定切换规则下的稳定性,得到了相应的时滞依赖稳定性结论;用Lyapunov泛函方法结合自由权重矩阵思想研究了带离散时滞的常时滞切换中立型系统的稳定性和L2增益,得到了基于平均驻留时间的时滞依赖指数稳定充分条件及L2增益条件;采用Lyapunov泛函方法结合自由权重矩阵思想研究了带离散时滞和分布时滞的常时滞切换中立型系统在一定切换规则下的稳定性,得到了系统的时滞依赖稳定性充分条件。
三、用Lyapunov泛函方法结合自由权重矩阵思想研究了含时变离散时滞的切换中立型系统的稳定性,得到了基于平均驻留时间的指数稳定充分条件;用Lyapunov泛函方法研究了含非线性扰动的变时滞切换中立型系统的稳定性,得到了基于平均驻留时间的指数稳定性条件。
四、分别用Lyapunov泛函方法和Lyapunov函数结合Razumikhin方法研究了切换非线性中立型系统的稳定性,得到了系统稳定的充分条件。
五、用Lyapunov泛函方法研究了脉冲切换中立型系统的稳定性,得到了系统稳定的矩阵不等式条件。
本文所得到的系统稳定性条件大多是以线性矩阵不等式表示的,可以直接在Matlab下的LMI工具箱实现。
Addressed in this dissertation is the stability analysis of switched neutral systems. Several relevant problems are discussed in detail,and a series of important results are obtained. As a whole, this dissertation is consisted of the following five aspects.
Firstly, by using the method of Lyapunov-Krasovskii functionals combining the technique of matrix inequalities and theory of weighted matrices, the delay-dependent stability of neutral systems with distributed- and discrete-delays is studied, and some less conservative results are obtained; by decomposing time delays, the stability of neutral systems with mixed delays and neutral systems with distributed- and discrete-delays is studied, based on a new class of Lyapunov-Krasovskii functionals introduced in this dissertation, combining the technique of matrix inequalities and theory of weighted matrices,some much less conservative results are obtained. The examples are supplied to illustrate the effectiveness of the results presented in this chapter.
Secondly, by applying the method of Lyapunov-Krasovskii functionals, combining the idea of weighted matrix and the method of equivalent system, the stability under some switched rules of a class of switched neutral system with discrete time-delay is studied, and some stability criteria are obtained; the stability and L2-gain of a class of switched neutral system with discrete delay are studied, and some sufficient conditions for exponential stability and L2-gain stability are acquired based on average dwell time; by applying the method of Lyapunov-Krasovskii functionals, combining the idea of weighted matrix,the stability under some switched rules of a class of switched neutral system with discrete and distributed-delays is studied, and some delay-dependent stability criteria under some switched rules are obtained.
Thirdly, by applying the method of Lyapunov-Krasovskii functionals, combining the idea of weighted matrix, the stability of a class of switched neutral system with timevarying discrete delayis studied, and some sufficient conditions of exponential stability are reached based on average dwell time; by applying the method of Lyapunov-Krasovskii functionals, the stability of a class of switched neutral system with time-varying delay and nonlinear perturbation is studied, and some exponential stability conditions are obtained based on average dwell time.
Fourthly, the methods of Lyapunov-Krasovskii functionals and Lyapunov-Krasovskii functions combining Razumikhinthe method are used to study the stability of a class of switched nonlinear neutral systems, and some sufficient conditions of stability are obtained.
Finally, the method of Lyapunov-Krasovskii functionals is used to study the stability of a class of impulsive switched neutral systems, and some stability criteria are obtained in term of matrix inequalities.
All the stability criteria are expressed in terms of linear matrix inequalities(LMIs), and they can realized in Matlab using the kit of LMIs.
引文
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