Stability analysis and state feedback stabilization of pendulum-like systems with multiple nonlinearities

This paper addresses the Lagrange stability analysis problem and the state feedback Lagrange stabilization problem for pendulum-like systems with multiple nonlinearities. An existing method for analysing the Lagrange stability of pendulum-like systems with a single nonlinearity is generalized to pendulum-like systems with multiple nonlinearities. Also, a non-degeneracy condition of the existing Lagrange stability criterion is removed and a strict frequency-domain inequality is used instead. To study the state feedback Lagrange stabilization problem, this paper develops an extended strict bounded real lemma for linear systems which are not stable but stabilizable. A sufficient condition for state feedback Lagrange stabilization is proposed in terms of an algebraic Riccati equation with a sign indefinite solution.     

时滞相关型离散时变时滞奇异系统的鲁棒镇定

讨论含参数不确定的离散时变时滞奇异系统的时滞相关的鲁棒状态反馈稳定化问题. 在一系列等价变换下, 阐述了其和一个不确定正常线性离散时变时滞系统的鲁棒状态反馈稳定化问题的等价关系;利用矩阵不等式方法, 给出一个对所有容许的不确定, 使得闭环系统正则、因果且稳定的时滞相关鲁棒状态反馈稳定化控制器存在的充分条件以及无记忆状态反馈控制器的一个解.     

Robust stabilization of nonlinear systems by H∞ state feedback

This paper is concerned with robust stabilization of nonlinear systems with unstructured uncertainty via state feedback. First, a robust stability condition is given for a closed loop system which is composed of a nonlinear nominal system and an unstructured uncertainty. Second, based on the obtained robust stability condition, a sufficient condition for robust stabilization by state feedback is given in terms of the solvability of some H_∞ state feedback control.     

不确定广义大系统有限时间鲁棒分散控制

研究不确定连续广义大系统的有限时间鲁棒分散控制问题,设计系统的有限时间鲁棒分散状态反馈控制器.首先应用广义Lyapunov 函数法,给出不确定广义大系统有限时间鲁棒稳定的充分条件;其次,给出不确定广义大系统应用分散状态反馈控制器鲁棒镇定的充分条件和有限时间鲁棒分散控制器的设计方法;最后,通过仿真例子验证所提出方法的有效性.     

Difference feedback can stabilize uncertain steady states

The paper is concerned with the stabilization of uncertain steady states by the state difference feedback. The feedback method has a peculiar feature that it uses only the difference between the present state x(t) and the past state x(t-T), considering exact information on the steady state is unavailable. Hitherto a condition is known under which such stabilization can not be realized. The article conversely shows that the state difference feedback can stabilize only if the exclusion condition is not true. Furthermore a dynamic output difference feedback is shown to be able to stabilize under quite a mild condition that the steady state is not associated with zero eigenvalues. The ability of the method is illustrated by using a cart-pendulum system which moves along a one dimensional varying slope     

基于观测器的时滞系统鲁棒控制器的设计

研究了一类不确定时滞系统基于观测器的鲁棒镇定问题,系统的不确定性时变未知且范数有界,目的是设计状态观测器和线性无记忆观测状态反馈控制器,使其能够镇定一类状态和控制输入不确定性时滞系统。基于Lyapunov稳定性理论,采用线形矩阵不等式这一有效工具,给出了系统基于观测状态反馈鲁棒镇定的充分条件,并且利用线形矩阵不等式的解构造了使得系统鲁棒稳定的基于观测状态反馈控制器,所得结果与时滞相关,从而相对减弱了控制器设计的保守性。数值算例表明了所提出的设计方法的有效性。     

一类不确定离散奇异系统的鲁棒稳定化

讨论了离散奇异系统矩阵E中含时不变参数不确定的鲁棒状态反馈稳定化问题.首先,在一系列等价变换下,阐述了其和一个不确定正常线性离散系统的鲁棒状态反馈稳定化问题的等价关系;然后,利用线性矩阵不等式(LMI)方法,给出了鲁棒状态反馈稳定化控制器存在的一个充分必要条件,控制器的设计方法及控制器的一个解;最后,通过一个数值算例验证了本设计方法的有效性.     

离散时滞切换系统的无记忆状态反馈镇定

针对一类子系统为离散时滞系统的切换系统,研究了稳定性与无记忆状态反馈镇定问题．采用多李雅普诺夫函数法,首先以线性矩阵不等式形式给出了在任意切换信号作用下离散时滞切换系统渐进稳定的一个充分性条件;然后给出了系统无记忆状态反馈镇定的控制器设计方案,并将结果推广到不确定离散时滞切换系统;最后用仿真算例验证了所提出设计方案的可行性。     

Further condition for the delay-independent stabilization of linear systems

There are two different conditions for the delay-independent stabilization of linear systems by means of state variable feedback including no delays, one of which is also sufficient for decay rate assignability. In this paper a wider condition is presented for delay-independent stabilization. It is proved that this condition includes the conditions so far obtained     

Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems With Time-Varying Delay

This paper is concerned with the problems of stability analysis and stabilization for discrete-time Takagi–Sugeno fuzzy systems with time-varying state delay. By constructing a new fuzzy Lyapunov function and by making use of novel techniques, an improved delay-dependent stability condition is obtained, which is dependent on the lower and upper delay bounds. The merit of the proposed stability condition lies in its reduced conservatism, which is achieved by avoiding the utilization of some bounding inequalities for the cross products between two vectors. Then, a delay-dependent stabilization approach based on a parallel distributed compensation scheme is developed for both state feedback and observer-based output feedback cases. The proposed stability and stabilization conditions are formulated in terms of linear matrix inequalities, which can be solved efficiently by using existing optimization techniques. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.      

不确定多时滞离散切换系统的输出反馈镇定

针对一类具有多重状态时滞和凸多面体不确定性的离散切换系统,研究该系统在任意切换信号下基于状态观测器的输出反馈鲁棒镇定问题.首先通过状态变量的替换将多时滞项转变成不含时滞项,再利用分段Lyapunov函数和线性矩阵不等式方法,导出凸多面体不确定多时滞离散切换系统基于观测器的输出反馈鲁棒镇定的充分条件,并将此条件转化成为一组线性矩阵不等式的可行性问题,同时给出基于状态观测器的输出反馈控制器.仿真结果表明设计方法是可行有效的.     

Minimum‐Time State Feedback Stabilization of Constrained Boolean Control Networks

Ministry in 2005, and the National Prize of Natural Science of China in 2008. Currently, he is Associate Editor IMA Journal of Math Control and Inform., and a Technical Committee member of IFAC (TC2.3). This paper investigates the state feedback stabilization of Boolean control networks (BCNs) with state and input constraints by using the semi‐tensor product of matrices. Firstly, a kind of constrained input‐state incidence matrix is proposed for constrained BCNs, which contains all the reachability information of the constrained systems. Secondly, based on the constrained input‐state incidence matrix, a necessary and sufficient condition is presented for the stabilization of constrained BCNs via state feedback. Thirdly, a general procedure is proposed to design all possible minimum‐time state feedback stabilizers. The study of an illustrative example shows that the new results obtained are effective in analyzing the stabilization of constrained BCNs.     

Robust Stabilization for Single-Input Polytopic Nonlinear Systems

This note deals with the stabilization problem of single-input polytopic nonlinear systems. The robust control Lyapunov function approach is used to derive a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controllers. The obtained sufficient condition is proven also necessary for the existence of stabilizing state feedback controllers such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. In addition, a universal formula for constructing stabilizing controllers when the presented sufficient condition is met is provided. The results are illustrated by a numerical example.     

State feedback control of a class of high‐order stochastic nonlinear systems

This paper poses and solves a new problem of state feedback stabilization for a class of high‐order stochastic nonlinear systems in which the power order restriction and growth condition are relaxed to a more general form. Based on the ideas of the homogeneous systems theory and the adding of a power integrator technique, a state feedback controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability and that the problem of inverse optimal stabilization in probability is solved. The efficiency of the state feedback controller is demonstrated by a simulation example. Copyright © 2011 John Wiley & Sons, Ltd.     

Simultaneous stabilization of a collection of single‐input nonlinear systems based on CLFs

This paper considers the simultaneous stabilization problem of a collection of single‐input nonlinear systems. Based on the technique of control Lyapunov functions (CLFs), a sufficient condition for the existence of a simultaneously stabilizing state feedback controller is proposed. It is shown that a collection of feedback linearizable systems in canonical form can be simultaneously globally asymptotically stabilized by a single state feedback controller. Moveover, for a set of three‐order chaotic dynamical systems, the simultaneous stabilization problem is considered and a similar result is derived. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Numerical examples are provided to illustrate the effectiveness of the proposed schemes. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Continuous stabilization controllers for singular bilinear systems: The state feedback case

Global asymptotic stabilization for a class of singular bilinear systems is first studied in this paper. New approaches are developed by means of the LaSalle invariant principle for nonlinear systems. A new set of sufficient condition is first derived via the continuous static state feedback, the feedback not only guarantees the existence of solution but also the global asymptotical stabilization for the closed loop system.     

同时镇定：逆LQ方法

本文使用逆ＬＱ方法了同时镇定问题，首先得到了ｒ个正则ＭＩＭＯ对象可静态输出反馈同时定的充要条件，然后给出了状态反馈问题同时镇定的一种解，这些条件均以一组耦合Ｒｉｃｃａｔｉ方程和Ｒｉｃｃａｔｉ不等式的形式给出，本语文证明，任一同时镇定反馈增益均可描述为一组具有合适交叉项的耦合ＬＱ控制问题的解。     

On the simultaneous stabilization of stochastic nonlinear systems

In this paper, the problem of simultaneous stabilization in probability by state feedback is investigated for a class of stochastic nonlinear systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Under the assumption that a collection of stochastic control Lyapunov functions (SCLFs) is known and based on the generalized stochastic Lyapunov theorem, we derive sufficient conditions for the simultaneous stabilization in probability by a continuous state feedback controller that we explicitly compute. We also derive a necessary condition when the system coefficients satisfy some regularity conditions. This work generalizes previous results on the simultaneous stabilization of stochastic nonlinear systems. The obtained results are illustrated by a numerical example.     

Almost Sure Stabilization of Uncertain Continuous-Time Markov Jump Linear Systems

This work deals with the robust Almost Sure (AS) stabilization problem for continuous-time Markov Jump Linear Systems (MJLS). Norm-bounded uncertainties affecting the system state and input matrices are considered. A deterministically testable sufficient condition for robust AS stability is provided which relies on a bound on the 2-norm of the system transition matrix. Such a condition can be profitably employed also to design a robust feedback stabilization strategy. Such feedback design is based on a formulation of the sufficient condition for robust AS stability in terms of an equivalent LMI problem.      

奇异摄动系统的鲁棒控制与仿真研究

研究参数不确定奇异摄动系统的状态反馈镇定问题,得到基于线性矩阵不等式（LMI）的系统状态反馈可镇定的充分条件,给出状态反馈控制器的设计算法。算例验证了该方法的可行性与有效性。而且,这种方法同时适用于标准奇异摄动系统和非标准奇异摄动系统的控制。最后通过例子进行了详细的仿真研究。