一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

随机非线性系统鲁棒自适应反馈控制器的积分反推方法设计

考虑了一类随机非线性系统的鲁棒自适应控制问题.采用Ito随机微分方程描述系统, 进而在概率意义下研究系统的鲁棒稳定性.应用积分反推(backstepping)方法,系统地给出了设 计状态反馈及输出反馈鲁棒自适应控制器的方法.同时构造出了适当形式的四次型的自适应控 制Lyapunov函数(CLF).     

基于S-Procedure的分段线性Delta算子系统的稳定性分析

本文研究了一类由Delta算子描述的分段线性系统的二次稳定性问题。基于Delta域的Lyapunov稳定性理论,利用S-procedure构造了分段Lyapunov函数,而且将分段线性Delta 算子系统的二次稳定性判问题转化为一组线性矩阵不等式的求解问题。     

单相UPQC的逆系统解耦控制器设计

单相统一电能质量调节器(single-phase unified power quality conditioner,SPUPQC)是一个强耦合的多输入多输出非线性系统.本文在平衡流形重构系统模型,基于逆系统方法对重构后的系统构造解耦的伪线性系统.针对该伪线性系统采用线性二次型调节器(LQR)设计了满足一定性能指标的控制器.该控制策略有良好的动态响应与补偿效果并有一定的实用价值.仿真实验证明了该控制器设计的可靠性与有效性.     

具有零动态仿射非线性系统控制Lyapunov函数的构造

研究具有零动态仿射非线性系统控制Lyapunov函数的构造问题.提出通过求解一个Lyapunov方程获得可线性化部分的二次型控制Lyapunov函数.由可线性部分的控制Lyapunov函数和零动态部分的Lyapunov函数,通过构造一个正定函数,得到了整个系统的控制Lyapunov函数,且设计了可半全局镇定整个闭环系统的控制律.仿真实例说明了所提出方法的有效性.     

基于分段Lyapunov 函数的Hammerstein-Wiener 非线性预测控制

针对输入和输出受约束的Hammerstein-Wiener型非线性系统,建立T-S模糊模型,并提出一种基于分段Lyapunov函数的非线性预测控制算法.通过构造分段二次Lyapunov函数,分析非线性系统的稳定性,降低普通二次Lyapunov函数的保守性;通过离线设计分段反馈控制律,在线实施符合条件的反馈控制律,极大程度地提高了在线计算效率.仿真结果验证了该方法的有效性.     

基于观测器的不确定广义时滞系统鲁棒预测控制

针对一类不确定广义时滞系统,讨论了其基于观测器的鲁棒预测控制问题,给出了系统观测器型预测控制器的设计方法.通过构造带有误差项的Lyapunov函数,应用线性矩阵不等式,将无穷时域二次性能指标"min-max"优化问题转化为凸优化问题,得到了鲁棒预测控制器存在的充分条件和显式表达式.证明了优化问题在初始时刻的可行解能保证广义闭环系统渐近稳定且正则无脉冲.仿真实例验证了所提出方法的有效性.     

三阶系统族的共同二次Lyapunov函数

研究了寻找三阶系统族的共同二次Lyapunov函数问题.针对给定的稳定的三阶系统提出了寻找二次Lyapunov函数集的方法,然后获得了三阶系统族具有共同二次Lyapunov函数的充分条件.该充分条件易于构造,从而具有较强的工程实用性.文中实例验证了所得结果的有效性.     

基于障碍Lyapunov函数的未知控制方向非线性系统的约束鲁棒输出调节

本文研究一类不确定非线性系统的约束鲁棒输出调节问题. 在具有未知控制输入方向的情况下, 要求被控线性系统的受控输出在趋近于零的同时, 被限制在给定的范围内. 文章结合障碍Lyapunov函数和Nussbaum增益技术, 进行反馈控制器的设计. 通过MATLAB仿真验证了控制算法的合理性. 同时, 与基于二次型Lyapunov函数设计的仿真结果进行对比, 表明了控制算法的有效性     

基于状态观测器的多面体不确定随机广义系统鲁棒预测控制

针对It?o型多面体不确定随机广义系统,提出一种离线观测器型鲁棒预测控制器的综合方法.通过构造带有误差项的增广随机Lyapunov函数,运用多维It?o公式和LMI方法,将“min-max”随机规划问题等价转化为一组线性矩阵不等式的求解问题;给出了控制器存在的充分条件和参数表达式,证明了初始时刻的可行解可以保证闭环广义系统的随机容许性.仿真算例验证了该方法的有效性.     

Composite quadratic Lyapunov functions for constrained control systems

A Lyapunov function based on a set of quadratic functions is introduced in this paper. We call this Lyapunov function a composite quadratic function. Some important properties of this Lyapunov function are revealed. We show that this function is continuously differentiable and its level set is the convex hull of a set of ellipsoids. These results are used to study the set invariance properties of continuous-time linear systems with input and state constraints. We show that, for a system under a given saturated linear feedback, the convex hull of a set of invariant ellipsoids is also invariant. If each ellipsoid in a set can be made invariant with a bounded control of the saturating actuators, then their convex hull can also be made invariant by the same actuators. For a set of ellipsoids, each invariant under a separate saturated linear feedback, we also present a method for constructing a nonlinear continuous feedback law which makes their convex hull invariant.     

Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions

This paper presents a stability analysis method for discrete-time Takagi-Sugeno fuzzy dynamic systems based on a piecewise smooth Lyapunov function. It is shown that the stability of the fuzzy dynamic system can be established if a piecewise Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software. It is also demonstrated via numerical examples that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions.     

Stability analysis and H infinity controller design of fuzzy large-scale systems based on piecewise Lyapunov functions.

This paper presents a novel approach to stability analysis of a fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno (T-S) fuzzy subsystems with interconnections. The stability analysis is based on Lyapunov functions that are continuous and piecewise quadratic. It is shown that the stability of the fuzzy large-scale systems can be established if a piecewise Lyapunov function can be constructed, and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. It is also demonstrated via a numerical example that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions. The H infinity controllers can also be designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions.     

Stability analysis and H/sub /spl infin// controller design of fuzzy large-scale systems based on piecewise Lyapunov functions

This paper presents a novel approach to stability analysis of a fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno (T-S) fuzzy subsystems with interconnections. The stability analysis is based on Lyapunov functions that are continuous and piecewise quadratic. It is shown that the stability of the fuzzy large-scale systems can be established if a piecewise Lyapunov function can be constructed, and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. It is also demonstrated via a numerical example that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions. The H/sub /spl infin// controllers can also be designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions.     

Non-conservative matrix inequality conditions for stability/stabilizability of linear differential inclusions

This paper shows that the matrix inequality conditions for stability/stabilizability of linear differential inclusions derived from two classes of composite quadratic functions are not conservative. It is established that the existing stability/stabilizability conditions by means of polyhedral functions and based on matrix equalities are equivalent to the matrix inequality conditions. This implies that the composite quadratic functions are universal for robust, possibly constrained, stabilization problems of linear differential inclusions. In particular, a linear differential inclusion is stable (stabilizable with/without constraints) iff it admits a Lyapunov (control Lyapunov) function in these classes. Examples demonstrate that the polyhedral functions can be much more complex than the composite quadratic functions, to confirm the stability/stabilizability of the same system.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for pieccwise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomiance and the controller can be obtained by solving a set of bilinear lnatrLx inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global qnadnmc Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

On the stability and control of nonlinear dynamical systems via vector Lyapunov functions

Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. In addition, we introduce the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. Moreover, using control vector Lyapunov functions, we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. Furthermore, we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law. Finally, the proposed control framework is used to construct decentralized controllers for large-scale nonlinear systems with robustness guarantees against full modeling uncertainty.