T-S离散模糊控制系统的二次稳定性研究

研究了Takagi-Sugeno离散模糊控制系统的二次稳定性问题。运用Lyapunov稳定性定理和线性矩阵不等式技术,在一个由模糊子系统的系数矩阵构成的负定矩阵中,充分考虑模糊子系统间的相互作用,得到了在并行分布补偿控制器作用下,闭环离散模糊系统二次稳定的充分条件。这些稳定性条件以线性矩阵不等式的形式给出,因而具有数值易解性。     

一种时滞相关非脆弱模糊控制器的设计

研究了一类带有时变时滞的离散模糊双线性系统的时滞相关非脆弱控制问题。引入自由权值矩阵并定义一种新型的Lyapunov函数,在控制器存在加性不确定的情况下,得到了保守性小的时滞相关渐近稳定的充分条件。通过附加矩阵,将所得到的稳定条件转换为线性矩阵不等式(linear matrix inequality, LMI)形式,非脆弱控制器可由LMI的解得到。数例仿真验证了该方法的有效性。     

模糊广义系统的稳定性分析

研究了模糊广义系统的二次稳定性问题,给出了使系统二次稳定的公共矩阵X存在的必要条件。在此基础上,通过线性矩阵不等式技术,得出了求解公共矩阵X的方法,与以往的结果相比,减少了求解过程的计算量。并给出了状态反馈控制器的设计以及相应的必要条件和求解方法。最后,通过数值例子验证了结论的正确性。     

离散模糊双线性关联大系统的广义H2分散控制

基于分段二次Lyapunov函数稳定性理论,研究了一类离散模糊双线性关联大系统广义H₂分散控制问题。模糊双线性关联大系统由J个相互关联的离散T-S模糊双线性系统组成。通过构造分段Lyapunov函数,给出了系统二次稳定的充分性条件。在此基础上,设计了广义H₂分散状态反馈控制器,使闭环系统广义H₂稳定,控制器的设计可以通过序列线性规划矩阵方法求解得到。仿真结果表明所提方法的有效性。     

不确定离散广义系统的保成本控制

针对一类具有范数有界时变参数不确定性的离散广义系统和二次成本函数,研究保成本控制律的设计问题。利用李雅普诺夫稳定性理论,得到了不仅使得闭环系统鲁棒二次稳定,而且闭环成本函数不超过某个确定上界的保成本控制存在的充分必要条件,并通过求解一个里卡蒂不等式给出了最优控制律的设计方法,最后通过数值例子说明方法的可行性。     

T-S模糊系统的鲁棒局部稳定

研究一类不确定T-S模糊系统的鲁棒局部稳定及鲁棒局部镇定问题。首先给出T-S模糊系统局部稳定的定义,并利用一种非二次Lyapunov函数得到T-S模糊系统鲁棒局部稳定的充分条件,然后给出一种新的非PDC控制器,进而利用非二次Lyapunov函数得到基于这种非PDC控制器的局部鲁棒镇定控制器设计方法。该方法基于线性矩阵不等式(LMI),结构简单,且具有较低的保守性。仿真算例证明了所提方法的可行性。     

时变时滞不确定系统模糊自适应H∞控制

针对含非线性和干扰项的时变时滞系统鲁棒稳定问题,提出一种模糊自适应H_∞控制方法。采用T-S模糊系统对未知非线性函数向量进行逼近,设计自适应全调节律,即同时调整模糊参数矩阵和基函数参量。对于逼近产生的误差和外界干扰,引入H_∞控制。基于李亚普诺夫稳定性理论和线性矩阵不等式技术,在保证系统稳定的前提下,通过求解矩阵不等式得到满足设计要求的控制器。通过对已有算例和空天飞行器高超声速飞行控制系统的仿真验证了所提方案的有效性。     

一类T-S 模糊广义系统的无源控制

研究了一类T-S模糊广义系统的无源控制问题.通过矩阵分解方法,证明了这类系统容许的充分必要条件.在此基础上,将严格无源的概念引入到T-S模糊广义系统中,得到了使闭环系统容许、严格无源的充分条件,并将此条件用线性矩阵不等式(LMIs)表示.通过解这些矩阵不等式得到状态反馈增益矩阵.这个充分条件,可以一次判定系统的容许、严格无源.最后的数值算例说明所给方法的可行、有效.     

T-S模糊控制系统稳定性分析及控制器设计

研究了在新型的模糊Lyapunov方法下连续T-S模糊控制系统稳定性和模糊控制器设计问题,首先,得出了自由系统新的稳定性充分条件,这个条件具有更大的宽松性;然后基于一系列线性矩阵不等式设计了模糊控制器,这些矩阵不等式可以利用凸优化技术来进行解决。通过对两个具体的实例的仿真验证了本算法的有效性。     

广义离散时变系统的Lyapunov稳定性

对于一类广义离散时变系统,通过Lyapunov方程的建立,给出了系统因果且渐近稳定的充分必要条件。接着利用Lyapunov不等式进一步研究了系统的稳定性问题,同时给出了系统因果且渐近稳定的另一个充分必要条件,该方法使得判断系统的稳定性更为方便。最后,给出了应用上述方法的具体步骤,通过举例说明了所得结果的正确性。     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems,the Takagi-Sugeno(T-S)fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay.Based on the linear matrix inequality(LMI)techniques and stability theory of stochastic differential equations,a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller.The resulting closed-loop fuzzy system is robustly reliable stochastically stable,and the corresponding quadratic cost function is guarauteed to be no more than a certain upper bound for all admissible uncertainties,as well as different actuator fault cases.A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented.Finally,a numerical simulation is given to illustrate the effectiveness of the proposed method.     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.     

Static output feedback control for discrete-time fuzzy bilinear system

The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system (DFBS) is presented.Based on parallel distribution compensation method,some sufficient conditions are derived to guarantee the stability of the overall fuzzy system.The stabilization conditions are further formulated into linear matrix inequality (LMI) so that the desired controller can be easily obtained by using the Matlab LMI toolbox.In comparison with the existing results,the drawbacks,such as coordinate transformation,same output matrices,have been eliminated.Finally,a simulation example shows that the approach is effective.     

Robust H∞ controller design for a class of nonlinear fuzzy time-delay systems

The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed. By using the linear matrix inequality (LMI) method, the problem of fuzzy robust H∞ controller design for the system is studied. Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory. By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.     

离散模糊时滞系统的鲁棒LQ/H∞非脆弱控制

针对一类由T-S模糊模型描述的不确定离散非线性时滞系统,讨论其在控制器存在可加性摄动情形下的鲁棒LQ/H_∞非脆弱控制问题。通过构造适当的Lyapunov函数,给出以线性矩阵不等式形式表示的系统时滞依赖稳定的充分条件以及相应的鲁棒LQ/H_∞非脆弱控制器设计方法。数值仿真表明,所构造的控制器不仅能够保证闭环模糊时滞系统的鲁棒渐近稳定性,还能使系统达到一定的H_∞干扰抑制水平。