一类非线性系统的有限时间保成本控制

针对一类具有有限能量外部扰动的连续不确定非线性系统,讨论其有限时间保成本控制问题。首先采用Takagi-Sugeno模糊模型对非线性系统进行建模,然后找到一个合适的Lyapunov函数,给出闭环模糊系统有限时间有界的充分条件及有限时间保成本控制器的设计方法,并将控制器的求解转化为一组线性矩阵不等式的可行性问题。研究表明,采用该方法设计的控制器不仅能使闭环不确定模糊系统对所有可允许的外部扰动是有限时间有界的,而且还给出了保成本上界的一个优化值。最后,仿真结果表明该设计方法是有效的。     

State and Output Feedback Finite-time Guaranteed Cost Control of Linear It Stochastic Systems

The problem of guaranteed cost control based on finite-time stability for stochastic system is first investigated in this paper.The motivation of solving this problem arises from an observation that finite/infinite-horizon guaranteed cost control does not consider the transient performance of the closed-loop system,but guaranteed cost control based on finite-time stability involves this practical requirement.In order to explain this problem explicitly,a concept of the stochastic finite-time guaranteed cost control is introduced,and then some new sufficient conditions for the existence of state and output feedback finite-time guaranteed cost controllers are derived,which guarantee finite-time stochastic stability of closed-loop systems and an upper bound of a quadratic cost function.Furthermore,this problem is reduced to a convex optimization problem with matrix inequality constraints and a new solving algorithm is given.Finally,an example is given to illustrate the effectiveness of the proposed method.     

Robust Finite-Time Guaranteed Cost Control for Positive Systems with Multiple Time Delays

This paper deals with the finite-time guaranteed cost control problem for positive system with multiple time delays and bounded disturbance. By using Lyapunov-Krasovskii functional method,some new sufficient conditions for the design of a state feedback controller which makes the closedloop system finite-time stable and guarantees an adequate cost level of performance are derived. Two numerical examples are also given to show the effectiveness of the proposed method.     

连续多时滞系统的保成本H∞容错控制

针对状态具有多个时滞的线性连续系统,基于Lyapunov稳定性理论和线性矩阵不等式方法,研究了在执行器发生故障的情况下,连续多时滞系统的保成本H_∞容错控制问题。首先,在无外部扰动时,得到了系统存在容错控制器的一个充分条件|其次,得到了系统存在保成本容错控制器的一个充分条件|最后,在有外部扰动时,得到了系统存在H_∞容错控制器的一个充分条件。进一步,得到了系统存在保成本H_∞容错控制器的一个充分条件以及该控制器的设计方法。仿真结果证明了该方法的正确性和有效性。     

参数不确定广义时滞系统的保性能控制

针对状态时滞的参数不确定性广义系统,讨论了它的保性能控制问题。目的是对状态时滞的参数不确定广义系统,提出它的时滞无关保性能鲁棒控制器的一个设计方法。首先给出了广义时滞系统正则、脉冲自由且稳定的严格线性矩阵不等式表示的时滞无关充分条件;然后采用线性矩阵不等式方法,给出参数不确定性广义时滞系统的时滞无关保性能控制问题可解的一个严格线性矩阵不等式表示的充分条件,在此条件可解时,给出了时滞无关保性能鲁棒控制器表达式,以及相应的可保性能指标。最后给出了所提出方法的应用。     

Guaranteed cost control for discrete-time networked control systems with random Markov delays

The guaranteed cost control for a class of uncertain discrete-time networked control systems with random delays is addressed.The sensor-to-controller (S-C) and contraller-to-actuator (C-A) random network-induced delays are modeled as two Markov chains.The focus is on the design of a two-mode-dependent guaranteed cost controller,which depends on both the current S-C delay and the most recently available C-A delay.The resulting closed-loop systems are special jump linear systems.Sufficient conditions for existence of guaranteed cost controller and an upper bound of cost function are established based on stochastic Lyapunov-Krasovakii functions and linear matrix inequality (LMI) approach.A simulation example illustrates the effectiveness of the proposed method.     

输入时滞Markov跳变系统鲁棒保性能控制及其仿真研究

研究一类具有模态相关时变输入和状态时滞的不确定马尔可夫跳变系统的鲁棒保性能控制问题。基于自由权矩阵方法,通过构造一个新的Lyapunov函数,给出了此类系统存在无记忆状态反馈鲁棒保性能控制律的充分条件,估计了其保性能值。并且,控制器的设计归结为一组LMI的求解问题。仿真实例说明了提出方法的有效性。     

不确定离散广义线性系统的保性能最优控制

对一类具有范数有界时不变参数不确定性的广义离散时间线性系统和一个二次型性能指标,研究了其最优保性能状态反馈控制律的设计问题。通过采用线性矩阵不等式方法,导出了存在保性能控制律的一个充分条件,进而证明了该条件可化为一个线性矩阵不等式的可解性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。在此基础上,通过建立并求解一个凸优化问题,给出了最优保性能控制律的设计方法,最后用例子说明了该方法的应用。     

时滞区间广义系统的保成本控制

针对一类具有状态时滞的时滞区间广义系统,基于状态反馈研究了保性能控制问题。利用线性矩阵不等式(LMI)处理方法,得到了闭环时滞区间广义系统广义二次稳定以及闭环性能指标值有上界的充分条件。利用LMI的可行解给出了保性能控制器的设计方法。设计的控制器使得闭环时滞区间广义二次稳定,同时保证闭环性能指标值是具有上界。最后的数值例子说明了所给方法的有效性。     

具有控制约束的不确定离散系统最优保性能控制

对一类具有范数有界时变参数不确定性和控制输入约束的离散时间线性系统,采用线性矩阵不等式处理方法,导出了保性能控制律存在的条件,证明了该条件等价于一组线性矩阵不等式的可行性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。进而,通过建立并求解一个凸优化问题,给出了具有控制约束的不确定离散系统最优保性能控制律设计方法。     

时变时滞不确定组合系统的可靠保性能鲁棒控制

针对一类孤立子系统中状态、控制输入及互联项均含有时变时滞的不确定组合系统,采用增益故障模型,提出了考虑执行器故障的可靠保性能控制问题。该执行器故障模型概括了执行器正常、执行器部分退化和执行器完全失效三种情况,系统的性能函数是带有故障输入项的积分二次函数。利用Lyapunov方法及线性矩阵不等式(LMI)方法,得到系统存在可靠保性能控制器的充分条件和控制器的设计方法,并给出了系统的可保性能表达式。最后,通过一个数值例子验证了所得结果的正确性。     

不确定时滞系统的指数稳定保代价可靠控制

针对一类含有时变时滞的不确定参数系统,研究了在执行器发生故障情况下系统指数稳定保代价可靠控制器设计问题。系统的性能函数是含有指数项和故障输入项的积分二次型函数。经过适当的状态变换,将原系统的指数稳定保代价可靠控制问题转化为另一个等价系统的保代价可靠控制问题。根据Lyapunov稳定性理论,得到了系统存在指数稳定保代价可靠控制器应满足的一个矩阵不等式,进一步将这个矩阵不等式转化为线性矩阵不等式(LMI),并给出了系统的保代价表达式。利用论文方法设计的控制器能够使得时滞系统对于任意允许的不确定量以及执行器故障都保持鲁棒可靠指数稳定,并且使系统具有保代价的性能指标。仿真结果表明了该控制器设计方法的有效性。     

一类模糊时滞系统的非脆弱H∞保成本容错控制

应用线性矩阵不等式方法研究TS模糊系统的H∞保成本容错控制器的设计问题。针对含有容许的不确定参数和可能的执行器故障的模糊时滞系统,在考虑保成本函数取得最小上界的基础上,兼顾系统的H∞性能。以线性矩阵不等式的形式给出TS模糊系统H∞保成本容错控制器存在的充分条件,把控制器的设计问题转化为线性矩阵不等式的可行解问题。通过例子验证了所给出的H∞保成本容错控制器设计方法的可行性和有效性。     

具有控制约束的不确定离散时滞系统最优保性能控制

对一类具有范数有界时变参数不确定性和控制输入约束的离散时滞系统,研究其最优保性能状态反馈控制律的设计问题.基于线性矩阵不等式处理方法,导出了保性能控制律存在的条件,并证明了该条件等价于一组线性矩阵不等式的可行性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示.进而,通过建立并求解一个凸优化问题,给出了具有控制约束的最优保性能控制律设计方法.     

含有跳变参数的中立系统的鲁棒保性能滤波

对一类含有马尔可夫跳变参数的中立系统研究了鲁棒保性能滤波问题。系统中含有时滞，跳变参数与不确定性。系统中的跳变参数可以通过有限状态马尔可夫过程来描述。目标是设计无记忆线性滤波器使得对所有的不确定性增广系统是时滞独立鲁棒随机稳定的，并且满足所提的保性能指标。基于随机微分方程稳定性理论，给出了线性滤波器存在的充分条件。借助一组相互关联的线性矩阵不等式，获得了鲁棒保性能的设计方法。通过求解线性矩阵不等式约束下的凸优化问题，给出了次优保性能滤波器的设计方法。     

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality (LMI) via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.     

不确定非线性广义系统的鲁棒控制与保性能控制

研究了不确定非线性结构扰动的广义系统的鲁棒控制和保性能控制问题,该不确定性为时间、状态函数且满足Lipschitz条件的。目的是分别设计系统的鲁棒控制器和保性能控制器。应用线性矩阵不等式方法,分别给出了系统的鲁棒控制器和保性能控制器存在的充分条件;并在这些条件可解时,分别给出了鲁棒控制器和保性能控制器的表达式。最后用例子说明了所给方法的应用。     

Stability and guaranteed cost control for uncertain time-delay Lur''''e systems

The problem of delay-dependent stability and guaranteed cost control （GCC） for a class of uncertain time-delay Lur＇e systems are studied. By using an improved integral inequality,a less conservative delay-dependent stability criterion is formulated as the feasibility problem of the linear matrix inequality （LMI）. The criterion is proved theoretically to be less conservative than some existing results for linear time-delay systems. Because of the fact that the matrices in the LMI-based stability criteria usually have different dimensions, different structures, and different variables, the conservatism analysis of the criteria is difficult. This study brings about a new insight into the comparison of conservatism among different stability criteria, which are expressed in certain LMI forms. The existence of the guaranteed cost controller is given in terms of matrix inequalities. The condition can be solved by using an iterative procedure and does not need any parameter tuning. A numerical example is given to illustrate the effectiveness of the proposed method.     

Robust guaranteed cost filtering for uncertain timedelay systems with Markovian jumping parameters

1.INTRODUCTION Itisnowwellknownthatstochasticmodelinghas cometoplayanimportantroleinmanybranchesof scienceandindustry.Anareaofparticularinterest hasbeenMarkovjumpsystems[1～5].Ontheother hand,stateestimationplaysanimportantroleinsys temsandcontroltheory,signalprocessingandinforma tionfusion.Certainly,themostwidelyusedestimation methodisthewell knownKalmanfiltering[6,7].Acom monfeatureintheKalmanfilteringisthatanaccurate modelisavailable.Insomeapplications,however,when thesystemissubject…