鲁棒输出反馈控制器设计

研究了满足匹配条件的 不 确定线性系统鲁棒输出反馈控制器的设计问题，。首先推导了受约束Ｌｙａｐｕｎｏｖ问题的两个构造性结论，基于此，给出输出反馈控制器的设计。最后的算例表明了该方法的有效性。     

一类不确定非线性系统的鲁棒输出反馈控制*

本文考虑一类具有输出反馈标准形的非线性系统的输出反馈控制问题，为了给出其不同于自适应控制的解决办法，设计出了新的鲁棒输出反馈控制方案。该方案不需辨识系统未知参数，也不需知识未知参数向量的上界，就能保证所有控制系统信号的全局有界性，并且顺参数的适当选择，可以使系统跟踪误差达到任意小。仿真结果表明可以获得良好的跟踪效果。     

广义离散系统的状态反馈鲁棒H∞控制

针对一类范数有界参数不确定性的广义离散线性系统,研究了该系统的状态反馈鲁棒H∞控制问题。利用线性矩阵不等式（LMI）的方法,得到了问题可解的条件,并给出了相应的状态反馈控制律。在一定条件下,所得的状态反馈鲁棒H∞控制律使广义离散线性系统对所有容许的不确定性参数,能够保证闭环系统正则、具有因果关系并且渐进稳定,同时其传递函数矩阵能够满足给定的H∞性能指标。正常离散线性系统的相对应结果可作为本文结果的特殊形式。     

线性时滞不确定系统的鲁棒稳定控制

对于线性时滞不确定系统，设计了一个新的鲁棒稳定控制器，文中就匹配与不匹配类不确定系统进行了研究。与现有一些方法相比，按本文方法设计的系统不但器增益较小，实现方便，而且可以容许较大的系统不确定性。     

线性时滞不确定系统的鲁棒稳定控制

对于线性时滞不确定系统,给出一种鲁棒渐近稳定控制器的设计方法,且对匹配与不匹配两类不确定系统进行了研究.与现有结果相比,按此方法设计的系统不但控制器增益较小,实现方便,而且可以容许较大的系统不确定性.     

一类时变系统鲁棒自适应状态反馈控制的稳定性分析

针对一类离散线性时变参数系统,给出了一种自适应状态反馈控制器,系统的时变参数是已知有界实函数和未知常数的线性组合,该控制器由带有死区的最小二乘辨识算法,状态反馈控制算法和状态观测器构成,文中详细地分析了闭环系统在有界外部干扰和小未建模不确定性影响下的全局稳定性和鲁棒性。     

一类离散时间切换系统鲁棒控制器设计

考虑一类非线性离散时间切换系统的鲁棒二次镇定和渐近镇定问题．利用公共李亚普诺夫函数方法和多李亚普诺夫函数方法，分别设计了切换系统鲁棒状态反馈控制器和输出反馈控制器，保证了切换系统的二次稳定性和渐近稳定性．仿真结果验证了所提出算法的有效性．     

离散双自由度鲁棒设计H∞方法研究*

以离散Ｈ∞全信息问题为基础，给出并证明了离散系统一类扰动前馈问题的设计方法，得到了控制器的参数化描述，在此基础上，研究了离散双自由度设计的Ｈ∞方法，在这一类问题中，相应标准离散Ｈ∞设计中的第二个离散代数Ｒｉｃｃａｔｉ方程不再需要求解，最后对精馏塔系统进行设计，得到了满意的结果。     

参数摄动系统的鲁棒LQ反馈控制

本文研究了不确定系统的鲁棒LQ反馈控制器的综合问题.对于具有线性有界实参数摄动的系统,首先把不确定系统的鲁棒LQ综合问题转化成N个确定系统的联立LQ综合问题.并据此提出了相应的综合算法.理论分析和实例计算结果表明所提出的方法具有较广的应用范围和较少的保守性.     

线性不确定系统的鲁棒稳定控制器设计

对于满足匹配条件的线性不确定系统,本文根据Lyapunov稳定性原理给出一种鲁棒稳定控制器的设计方法,这种方法可以设计鲁棒稳定控制器对于标称系统是最优的.本文还将这种方法推广到不满足匹配条件的线性不确定系统,并给出数值例子说明了这种方法的有效性.     

On robust stability of discrete-time adaptive nonlinear control

We consider adaptive control of discrete-time nonlinear systems with a single unknown parameter in this paper. We demonstrate that the necessary and sufficient condition for the existence of a feedback stabilizer that is robust to bounded noise is that the nonlinear growth rate of the system dynamics is less than 4. This result further confirms the conclusion of Guo [On critical stability of discrete-time adaptive nonlinear control, IEEE Trans. Automat. Control 42 (1997) 1488–1499] which addresses unbounded noise in a stochastic setting. Also in our worst-case approach, we find that much simpler adaptive stabilizers can be constructed when the nonlinear growth rate is less than 4.     

A new LMI condition for robust stability of discrete-time uncertain systems

In this paper, a new robust stability condition is derived for uncertain discrete-time linear systems with convex polytopic uncertainties. The condition is expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine robust stability of uncertain systems easily by solving some LMIs. A rigorous proof is given to show that an interesting result appeared recently is a special case of the proposed condition. Numerical examples also demonstrate the merit of the present condition in the aspect of conservativeness over other results in the literature.     

An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.     

An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties.A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix.Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases.A numerical example illustrates the improvement over the existing ones.     

An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.     

A less conservative LMI condition for the robust stability of discrete-time uncertain systems

In this paper, a less conservative condition for the robust stability of uncertain discrete-time linear systems is proposed. The uncertain parameters, assumed to be time-invariant, are supposed to belong to convex bounded domains (polytope type uncertainty). The stability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope domain. A simple and numerically efficient feasibility test provides a set of Lyapunov matrices whose convex combination can be used to assess the stability of any dynamic matrix inside the uncertainty domain. Examples illustrate the results.     

Establishing robust stability of discrete-time systems with time-varying uncertainty: The Gram-SOS approach

This paper addresses the problem of establishing robust asymptotical stability of discrete-time linear systems polynomially affected by time-varying uncertainty confined into a polytope. A linear matrix inequality (LMI) condition for establishing robust asymptotical stability is proposed by introducing a novel approach for establishing the existence of a common homogeneous polynomial Lyapunov function (HPLF). This approach consists, firstly, of introducing a Gram matrix built with respect to the state and parametrized by an arbitrary vector function of the uncertainty, and secondly, of requiring that a transformation of the introduced Gram matrix is a sum of squares (SOS) of matrix polynomials. The approach, hence, is referred to as a Gram-SOS approach. It is shown that the proposed LMI condition is sufficient for any degree of the HPLF candidate, that includes quadratic robust stability as a special case, and that is also necessary for a sufficiently large degree of the HPLF candidate. Numerical examples also show that the proposed LMI condition can outperform alternative ones in terms of conservatism and computational burden.     

Improved robust backstepping adaptive control for nonlinear discrete-time systems without overparameterization

This paper reports a robust backstepping adaptive controller for output tracking of nonlinear discrete-time systems. The result improves the previous one in Zhang, Wen, and Soh [(2001). Robust adaptive control for nonlinear discrete-time systems without overparameterization. Automatica, 37, 551-558] by removing the lower bound constraints on the system nonlinearities.     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with °- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper.