不确定广义系统的第一类鲁棒稳定性分析
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摘要
广义系统的鲁棒稳定就是对于所有容许的不确定性仍能使系统保持其稳定性,即稳定且无脉冲的性能。广义系统的鲁棒稳定性分析与控制是广义系统鲁棒控制的一个基本问题。本文讨论了具有不确定性的广义系统的第一类稳定性问题,改变系统的受限等价形式,选取李雅普诺夫方程,在不确定广义系统的标称广义系统是容许的条件下,求得使广义不确定系统鲁棒稳定的不确定性的最大扰动范围。
The robust stability of the generalized system is to keep the system stable,same as stable and without pulse,for all the allowable uncertainties.The robust stability analysis and control of the generalized system is a basic problem for robust control of the generalized system. In this paper,the first kind of stability problem of the generalized system with the uncertainty is discussed,the limited equivalent form of the system is changed,the Lyapunov equation is selected,and under the condition that the nominal generalized system of the generalized system is not determined to be allowable,The maximum perturbation range of the uncertainty of the robust stability of the generalized uncertain system is obtained.
The robust stability of the generalized system is to keep the system stable,same as stable and without pulse,for all the allowable uncertainties.The robust stability analysis and control of the generalized system is a basic problem for robust control of the generalized system. In this paper,the first kind of stability problem of the generalized system with the uncertainty is discussed,the limited equivalent form of the system is changed,the Lyapunov equation is selected,and under the condition that the nominal generalized system of the generalized system is not determined to be allowable,The maximum perturbation range of the uncertainty of the robust stability of the generalized uncertain system is obtained.
引文
[1]张庆灵,樊治平.广义系统的Lyapunov方程[J].东北大学学报,1997,18(1):21-25.
[2]徐胜元.广义不确定系统的鲁棒控制[D].南京理工大学,1999.
[3]杨冬梅,张庆灵,姚波.广义系统[M].北京:科学出版社,2004.
[4]俞立.线性系统的鲁棒稳定性分析[J].自动化学报,2010,27(6):850-862.
[5] Sun F Q,Yang C Y, Zhang Q L,et al.Stability bound analysis and design of singularly perturbed systems with time-varying delay[J].Mathematical Problems in Engineering,2013(1):61-68.
[2]徐胜元.广义不确定系统的鲁棒控制[D].南京理工大学,1999.
[3]杨冬梅,张庆灵,姚波.广义系统[M].北京:科学出版社,2004.
[4]俞立.线性系统的鲁棒稳定性分析[J].自动化学报,2010,27(6):850-862.
[5] Sun F Q,Yang C Y, Zhang Q L,et al.Stability bound analysis and design of singularly perturbed systems with time-varying delay[J].Mathematical Problems in Engineering,2013(1):61-68.