摘要
中立型随机时滞系统近年来逐渐受到研究人员的关注。目前,对于中立型随机时滞系统控制理论方面的研究已取得了一定成果,但与确定性中立型时滞系统较完善的研究成果相比,还有一些有待解决的问题。本文利用随机分析学理论,在Lyapunov稳定性理论框架下,对不确定中立型随机时滞系统的鲁棒稳定性、H_∞滤波、保性能控制、H_∞控制、非脆弱控制、非脆弱滤波等方面作了研究,主要研究内容概括如下:
1、研究了不确定中立型随机时滞系统的时滞相关稳定性问题,利用随机分析学的知识,通过引入适当的自由权矩阵,得到了时滞相关的稳定性条件。在得到稳定性条件时,充分利用随机分析学的知识尤其是It(?)积分的性质,引入了适当的自由权矩阵,避免了对Lyapunov函数的弱无穷小算子进行放大,从而降低了稳定性条件的保守性。通过数值例子对该结论与已有结果进行了比较,验证了本文结果的保守性更小。
2、研究了不确定中立型随机时滞系统的鲁棒H_∞滤波问题。首先,在时滞相关稳定性的基础上,对不确定中立型随机时滞系统,通过引入自由权矩阵,给出了时滞相关的有界实引理。基于该有界实引理,给出了不确定中立型随机时滞系统H_∞滤波器存在的时滞相关的充分条件。然后,利用以上方法还研究了一类不确定非线性中立型随机时滞系统的鲁棒H_∞滤波问题。并通过仿真例子验证了方法的有效性。
3、研究了一类不确定非线性中立型随机时滞系统的保性能控制问题。利用Lyapunov稳定性理论和It(?)公式,设计出状态反馈控制器使得相应的闭环系统是鲁棒均方随机渐近稳定的且对于所有不确定性,性能函数有一个上界。并用仿真算例验证了该方法的有效性。
4、研究了具有分布时滞的不确定中立型随机时滞系统的鲁棒H_∞控制问题与非脆弱H_∞控制问题。首先,对于具有分布时滞的不确定中立型随机时滞系统,给出了H_∞控制器存在的充分条件,并将上述结果推广到一类具有分布时滞的不确定非线性中立型随机时滞系统。然后,对于具有分布时滞的中立型随机时滞系统的H_∞控制问题,给出了非脆弱控制器的设计方法,即设计的控制器在实际应用中当其参数发生一定变化时,仍能保证相应的闭环系统保持稳定和满足给定的H_∞性能。最后,通过数值仿真验证了该方法的有效性。
5、对一类具有分布时滞的不确定中立型随机变时滞系统,研究了其非脆弱H_∞滤波器的设计问题,即设计的滤波器在实际应用中当其参数发生一定变化时仍能保证滤波误差系统是均方随机渐近稳定的且满足给定的H_∞性能。然后,对于第三章的中立型随机时滞系统的H_∞滤波问题,通过引入自由权矩阵,给出了时滞相关的非脆弱H_∞滤波器存在的充分条件。
Recently,neutral stochastic time-delay systems have attracted researchers' interesting,and some results about neutral stochastic time-delay systems have been given.However,there are still some problems which have not been fully investigated. Making use of the knowledge of stochastic analysis and the theory of the Lyapunov stability,the dissertation provides some results on robust stability,robust H_∞filtering, guaranteed cost control,robust H_∞control,non-fragile control,non-fragile filtering for uncertain neutral stochastic time-delay systems.The main results obtained in this dissertation are as follows:
1、The robust stability problem for uncertain neutral stochastic time-delay systems is considered.By using the knowledge of stochastic analysis and introducing the free weighting matrix,a delay-dependent condition,that guarantees the uncertain neutral stochastic time-delay systems to be robust stochastically stable,is proposed. When obtaining this condition,we don't use any bounding technique to deal with the weak infinitesimal operator of the Lyapunov function by using the knowledge of stochastic analysis.Therefore this condition is less conservative than the existing one in the literature,which is demonstrated by numerical examples.
2、The problem of delay-dependent robust H_∞filtering for uncertain neutral stochastic time-delay systems is studied.Based on the delay-dependent stability condition in the first part,a delay-dependent bounded real lemma is obtained by introducing the free weighting matrix.Then,a delay-dependent condition for the solvability of the robust H_∞filtering problem is proposed,and the H_∞filter is designed.After this,the problem of robust H_∞filtering for a class of uncertain nonlinear neutral stochastic time-delay systems is also studied.The numerical example is provided to demonstrate the effectiveness of the proposed approach.
3、The dissertation considers the problem of guaranteed cost control for a class of uncertain nonlinear neutral stochastic time-delay systems.In terms of the theory of the Lyapunov stability and It(?)formula,a state feedback controller is designed such that the closed-loop system is mean-square asymptotically stable and the value of cost function is not larger than a special bound.A numerical example is given to demonstrate the effectiveness of the developed approach.
4、The dissertation also considers the robust H_∞problem and non-fragile H_∞problem for uncertain neutral stochastic systems with distributed delays.Firstly, a state feedback controller is designed for the uncertain linear neutral stochastic systems with distributed delays.Secondly,the robust H_∞control problem of a class of uncertain nonlinear neutral stochastic systems with distributed delays is investigated.Thirdly,we considered the H_∞control problem for uncertain neutral stochastic systems with distributed delays via non-fragile controllers,i.e.,the controllers can stabilize the systems and satisfy the H_∞performance even if the controllers are perturbed externally.The numerical example is provided to demonstrate the effectiveness of the proposed approach.
5、The problem of non-fragile H_∞filtering for uncertain neutral stochastic systems with distributed delays is considered.Attention is focused on the design of a filter which is subject to norm-bounded uncertainties,such that the filtering error system is mean-square asymptotically stable with a prescribed H_∞performance level for all admissible uncertainties.And we also consider the non-fragile H_∞filtering problem for the neutral stochastic time-delay systems in chapter 3;a delay-dependent condition for the solvability of the non-fragile H_∞filtering problem is also proposed by introducing the free weighting matrix.
引文
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