线性时滞系统的耗散控制

研究了一类线性时滞系统的二次耗散控制问题,基于线性矩阵不等式（LMI）方法导出了耗散控制器存在的充分条件,通过线性矩阵不等式的可行解构造出耗散态状态反馈和动态输出反馈控制律,相应的闭环系统是二次稳定和严格（Q,S,R）耗散的,本文的主要贡献是统一了线性时滞系统现有的H∞控制和无源控制结果。     

线性离散时滞系统的输出反馈耗散控制

考虑线性离散时滞系统的二次型耗散控制问题,设计动态输出反馈使闭环系统渐近稳定且严格二次型耗散.先将系统严格二次型耗散性转化为线性矩阵不等式的可解性,得到了系统渐近稳定且严格二次型耗散的条件.然后讨论输出反馈耗散控制问题,给出了控制器的存在条件,总结出了控制器的综合方法、步骤.所得结果可为离散时滞系统的无源控制和H∞控制提供统一框架,也为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

离散广义系统的严格耗散分析与控制

对离散广义系统,考虑了关于二次型供给率严格耗散控制问题.建立了严格耗散与扩展严格正实之间的等价性.利用线性矩阵不等式(LMI),给出了离散广义系统严格耗散的充分必要条件,并着重推导了其成立的严格LMI条件.针对输入向量维数等丁状态向量维数的系统,分别利用非严格LMI及严格LMI,讨论了状态反馈下的严格耗散控制问题,并给出控制器的设计方法.也讨论了输入向量维数小于状态向量维数的情况.最后通过仿真算例说明所给方法的有效性和普遍性,同时显示了严格LMI条件在耗散控制问题中,比非严格LMI具有的优势.     

二次型耗散线性离散系统的鲁棒性分析与控制

考虑一类不确定离散多变量系统的鲁棒二次型耗散性分析和控制,其中各不确定参数矩阵具有线性分式形式.首先对确定系统建立二次型耗散性与正实性之间的等价关系,由此导出线性系统二次型耗散的充分必要条件;然后证明不确定系统的鲁棒耗散性分析和控制可转化为确定系统的耗散性分析和设计,给出了这类不确定系统鲁棒耗散的充分必要条件以及鲁棒耗散控制问题的线性矩阵不等式解法.所得结果可将H∞控制与正实控制统一起来,提供一种较为灵活、保守性较小的系统设计方法.仿真例子说明了所提方法的有效性.     

线性广义系统基于一般形式观测器的严格耗散控制

本文主要研究线性广义系统基于一般形式状态观测器的严格耗散控制器的设计问题,其中关于状态观测器需要同时设计3个系数矩阵.利用线性矩阵不等式方法,分别得到了满足要求的状态观测器及严格耗散控制器的存在条件及设计方法,保证观测器能够渐近地跟踪系统状态并且闭环广义系统容许且严格耗散.最后给出两个数值算例说明本文设计方法的有效性.     

不确定时滞双线性广义系统的鲁棒耗散控制

针对带有耗散不确定性的时滞双线性广义系统的鲁棒耗散控制问题,首先将耗散不确定性引入双线性广义系统,利用线性矩阵不等式方法给出系统鲁棒稳定且严格耗散的充分条件;然后利用线性矩阵不等式的解,构造出闭环系统鲁棒耗散的状态反馈控制器;最后通过数值算例验证了所得结论的可行性.     

带非线性摄动的状态延迟系统的H∞鲁棒控制

研究了带非线性摄动的状态延迟系统的H∞鲁棒控制.该摄动用有界范数描述,它 不仅与非延迟状态有关,而且与延迟状态有关.用动态耗散理论,基于矩阵不等式,给出了系 统满足H∞鲁棒扰动衰减性能准则的充分条件;同时系统地推导出了独立于延迟的无记忆状 态反馈控制器、基于状态观测器的动态输出反馈控制器和依赖于延迟的状态反馈控制器的设 计算法.     

基于LMI方法的T-S模糊系统的

研究一类T-S模糊系统的动态输出反馈耗散控制问题．给出了保证该系统耗散的动态输出反馈控制器的设计方法．动态输出反馈耗散控制器可通过求解一组线性矩阵不等式（LMI）获得．最后通过仿真例子说明了所提出的设计方法的有效性．     

线性离散时滞系统的鲁棒耗散控制

考虑线性离散时滞系统的二次型耗散控制问题.对于确定系统,给出渐近稳定且严格二次型耗散的条件和动态输出反馈控制器使闭环系统渐近稳定且严格二次型耗散.对于不确定系统,考虑不确定性具有耗散特性的情形,讨论鲁棒耗散性分析和动态输出反馈鲁棒耗散控制问题.通过构造增广系统,将不确定系统的鲁棒严格二次型耗散分析和设计转化为确定系统的情况.所得结果为离散时滞系统的无源控制和H∞控制提供了统一框架,且为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

连续T-S模糊系统的严格二次型耗散控制

研究一类连续Ｔ-Ｓ模糊系统的严格二次型耗散控制问题,给出了保证系统严格二次型耗散稳定的状态反馈控制器的设计方法．控制器可通过求解一组线性矩阵不等式获得,所得结果不仅提供了解决犎∞ 控制与正实控制的统一框架,而且提供了一种更灵活、保守性更小的控制器设计方法．最后通过仿真说明了所提出方法的有效性、可行性和优越性．     

一类多不确定性系统鲁棒H∞控制器的LMI设计方法

对同时具有加型参数不确定性以及积分二次约束(IQC,integral quadratic constraint) 不确定性环节的一类线性系统,给出设计其鲁棒H∞状态反馈控制器和动态输出反馈降阶控制 器的设计方法.在具体推导过程中,首先基于动态耗散理论,考虑了无输入情况下系统只具不 确定性闭环环节时的鲁棒H∞稳定性问题.然后基于这一条件,针对典型的无源类和有限增益 类不确定性,推出了系统同时具有多不确定性时进行鲁棒H∞状态反馈控制器和动态输出反馈降 阶控制器设计的充分条件.所有可解条件都可化为标准的LMI(1inear matrix inequality)求解.     

Generalised observer design for dissipative Lipschitz nonlinear systems in the presence of measurement noise

This paper presents two novel observer concepts. First, it develops a globally exponentially stable nonlinear observer for noise-free dissipative nonlinear systems. Second, for a dissipative nonlinear system with measurement noise, the paper develops an observer to guarantee a desired performance, namely an upper limit on the ratio of the square of the weighted L2 norm of the error to the square of the weighted L2 norm of the measurement noise. The necessary and sufficient conditions for both observers are reformulated as algebraic Riccati equations (AREs) so that standard solvers can be utilised. In addition, the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the ARE (and hence the observer design problem) has a solution. The use of the methodology developed in this paper is demonstrated through illustrative examples. In literature, there is no previous observer for dissipative system that provides both necessary and sufficient conditions. Results for noisy system either rely on linearising the system about state trajectory (requiring initial estimates to be close to the actual states) or are for specialised systems that cannot be extended to dissipative systems.     

线性多变量系统的鲁棒耗散控制

Robust quadratic dissipative control for a class of linear multi-variable systems with parameter uncertainties is considered, where the uncertainties are expressed in a linear fractional form. For the nominal system without uncertainties, the equivalence between quadratic dissipativeness and positive realness is established, and conditions are derived for linear systems to be quadratic dissipative. As for uncertain systems, it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties. The control problem concerned can be solved using LMI approach. The results of the paper unify existing results on H1 control and positive real control and provide a more flexible and less conservative control design method.     

一类非线性广义系统的时滞相关耗散控制

针对一类带有非线性摄动的广义时滞系统,研究了时滞相关的鲁棒耗散问题.讨论了此类非线性广义时滞系统的鲁棒耗散性.同时对此类非线性广义时滞系统的二次稳定性进行了研究,分别用线性矩阵不等式（LMI）的方法给出了充分条件,也给出了时滞相关的鲁棒耗散的时滞上界.并且,给出了时滞相关的鲁棒耗散的状态反馈控制器.最后,通过例子验证了定理的可行性.     

Feedback stabilization of dissipative impulsive dynamical systems

In this paper, we derive conditions under which a dissipative impulsive dynamical system is asymptotically stabilizable by a feedback controller. Specializing the obtained results to the case of dissipative linear impulsive dynamical systems with the quadratic supply rate, we establish the corresponding sufficient conditions. Finally, simulation results are given to demonstrate the effectiveness of our results.     

基于PI 控制器的线性系统的鲁棒耗散控制

针对参数具有确定性及不确定性的连续系统,给出两种严格耗散PI控制器的设计方法.首先,系统参数确定时,采用线性矩阵不等式方法,导出了类状态反馈和静态输出反馈严格耗散PI控制器存在的充要条件,并由线性矩阵不等式的可行解构造出严格耗散PI控制器增益的显式表达式;然后,考虑系数矩阵均具有范数有界不确定性时的鲁棒严格耗散控制问题,得到相似的结果;最后,通过数值算例表明了所给方法的有效性.     

不确定非线性系统的鲁棒耗散性与保性能控制

考虑了不确定仿射非线性系统的鲁棒耗散性与保性能控制问题,不确定性范数有界,不满足匹配条件.基于HJI不等式,设计了状态反馈控制器.当扰动存在时,控制器能使系统达到耗散,当扰动为零时,所设计的控制器使系统对于给定的性能函数具有上界,最后研究了不确定线性系统的保性能与耗散性控制情形.     

Problems on time-varying port-controlled Hamiltonian systems: geometric structure and dissipative realization

To apply time-varying port-controlled Hamiltonian (PCH) systems to practical control designs, two basic problems should be dealt with: one is how to provide such time-varying systems a geometric structure to guarantee the completeness of representations in mathematics; and the other is how to express the practical system under consideration as a time-varying PCH system, which is called the dissipative Hamiltonian realization problem. The paper investigates the two basic problems. A suitable geometric structure for time-varying PCH systems is proposed first. Then the dissipative realization problem of time-varying nonlinear systems is investigated, and serval new methods and sufficient conditions are presented for the realization.     

Study on the stability of switched dissipative Hamiltonian systems

The hybrid Hamiltonian system is a kind of important nonlinear hybrid systems. Such a system not only plays an important role in the development of hybrid control theory, but also finds many applications in practical control designs for obtaining better control performances. This paper investigates the stability of switched dissipative Hamiltonian systems under arbitrary switching paths. Under a realistic assumption, it is shown that the Hamiltonian functions of all the subsystems can be used as the multiple-Lyapunov functions for the switched dissipative Hamiltonian system. Based on this and using the dissipative Hamiltonian structural properties, this paper then proves that the P-norm of the state of switched dissipative Hamiltonian system converges to zero with the time increasing, and presents two sufficient conditions for the asymptotical stability under arbitrary switching paths. Utilizing these new results, this paper also obtains two useful corollaries for the asymptotical stability of switched nonlinear time-invariant systems. Finally, two examples are studied by using the new results proposed in this paper, and some numerical simulations are carried out to support our new results.