Stability analysis and stabilization for discrete-time singular delay systems

Stability analysis and stabilization for discrete-time singular delay systems are addressed,respectively.Firstly,a sufficient condition for regularity,causality and stability for discrete-time singular delay systems is derived.Then,by applying the skill of matrix theory,the state feedback controller is designed to guarantee the closed-loop discrete-time singular delay systems to be regular,casual and stable.Finally,numerical examples are given to demonstrate the effectiveness of the proposed method.     

New criteria on delayed state feedback stabilization for stochastic systems with time-varying delay

The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied.By using Jensen’s integral inequality and combining with the free weighting matrix approach,new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities.Meanwhile,the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved.Numerical examples are given to illustrate the effectiveness of the proposed methods.     

Robust stability and stabilization for uncertain discrete-time switched singular systems with time-varying delays

The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated. By constructing a novel switched Lyapunov–Krasovskii functional, a delay-dependent criterion for the unforced system to be regular, causal and uniformly asymptotically stable is established in terms of linear matrix inequalities (LMIs). An explicit expression for the desired memoryless state feedback stabilization controller is also given. The merits of the proposed criteria lie in their less conservativeness and relative simplicity, which are achieved by considering additionally useful terms (ignored in previous methods) when estimating the upper bound of the forward difference of the Lyapunov–Krasovskii functional and by avoiding utilizing any model augmentation transformation. Some numerical examples are provided to illustrate the validity of the proposed methods.     

Adaptive stabilization for cascade nonlinear systems

An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF) techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.     

不确定时滞组合系统的分散输出反馈镇定

综合运用比较原理和LMI方法,通过构造一比较系统,将原组合系统的稳定性问题转化为讨论维数低的比较系统的稳定性问题,并利用M矩阵特性导出了比较系统稳定的一个充分条件;为了求取输出反馈增益,建立了等价的稳定条件的QLMI表示形式。通过建立QMI中一矩阵变量的递推关系,将QMI问题转换为一替代过程的LMI求解问题,进而通过求解这一LMI问题来获取可镇定的非线性组合系统输出反馈增益阵。这一方法的特点是使大系统的稳定控制器设计的复杂度保持在子系统一级的水平上,给出实例说明了算法在实际工程应用中是有效的。     

高阶随机非线性系统状态反馈镇定

针对一类高阶下三角随机非线性系统,提出一种新的镇定方案,采用增加一个幂积分的工具构建了一个全局稳定的光滑状态反馈控制律。通过反馈占有设计方法和Young不等式处理随机系统的非线性项,取消了对随机非线性系统反馈线性化和控制输入呈线性的要求,基于Lyapunov方法,证明了闭环系统依概率全局渐近稳定。最后,仿真实例说明了算法的可行性。     

一类转移概率部分未知的Markov跳跃系统的输入输出量化反馈控制

对一类离散时间马尔可夫跳跃系统(Markov jump systems,MJSs)的稳定性问题进行研究,考虑MJSs转移概率矩阵中的元素部分未知,且系统的控制输入通道和测量输出通道都存在信号量化的情况,其中控制器输入通道和系统输入通道的信号分别被两个不同的对数量化器量化。利用切换李雅普诺夫函数的方法,通过构造系统模态依赖且双通道量化误差依赖的李雅普诺夫函数,完成对闭环系统的稳定性分析和控制器设计。得到一组模态依赖的控制器,能够在系统的转移概率部分未知和存在双通道量化误差的条件下,保证闭环MJSs的随机稳定性。最后通过仿真实验验证了理论的有效性。     

Quantized dynamic output feedback control for networked control systems

The problem of the quantized dynamic output feedback controller design for networked control systems is mainly discussed. By using the quantized information of the system measurement output and the control input, a novel networked control system model is described. This model includes many networkinduced features, such as multi-rate sampled-data, quantized signal, time-varying delay and packet dropout. By constructing suitable Lyapunov-Krasovskii functional, a less conservative stabilization criterion is established in terms of linear matrix inequalities. The quantized control strategy involves the updating values of the quantizer parameters μi(i = 1, 2)(μi take on countable sets of values which dependent on the information of the system measurement outputs and the control inputs). Furthermore, a numerical example is given to illustrate the effectiveness of the proposed method.     

Finite time stability and stabilization of hybrid dynamic systems

Finite time stability and stabilization are studied for hybrid dynamic systems. By combining multiple Lyapunov function and finite time Lyapunov function, a sufficient condition of finite time stability is given for the system. Compared with the previous works, our results have less conservativeness. Furthermore, based on the state partition of continuous and resetting parts of system, a hybrid feedback controller is constructed, which stabilizesthe closed-loop systems in finite time. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

区间离散广义系统输出反馈鲁棒H∞控制

讨论了区间离散广义系统的静态输出反馈鲁棒H∞控制问题,在给出区间离散广义系统的等价描述之后,基于系统参数矩阵不等式,得到了问题可解的充分条件,并给出了输出反馈控制器显式表示,所得控制器保证闭环系统是容许的,且满足给定的H∞性能指标,数值例子说明了该方法的可行性。     

State feedback stabilization for a class of nonlinear time-delay systems via dynamic linear controllers

The dynamic linear state feedback control problem is addressed for a class of nonlinear systems subject to time-delay. First, using the dynamic change of coordinates, the problem of global state feedback stabilization is solved for a class of time-delay systems under a type of nonhomogeneous growth conditions. With the aid of an appropriate Lyapunov-Krasovskii functional and the adaptive strategy used in coordinates, the closed-loop system can be globally asymptotically stabilized by the dynamic linear state feedback controller. The growth condition in perturbations are more general than that in the existing results. The correctness of the theoretical results are illustrated with an academic simulation example.     

Delay-dependent state feedback robust stabilization for uncertain singular time-delay systems

The problem of robust stabilization for uncertain singular time-delay systems is studied.First,a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given,which is less conservative.Using this result,the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed.Finally,two examples are given to illustrate the effectiveness of the results.     

Robust passive control for discrete-time T-S fuzzy systems with delays

This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality (LMI) method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive.  urthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.     

Robust H∞ control for uncertain stochastic saturating systems with time delays

The robust H∞ control problem for uncertain stochastic time-delay systems containing nonlinear actuators is considered. The uncertainties in the systems are assumed to satisfy specific match condition. The time delays exitst in state as well as control input. The new stochastic robust stabilization criterion and a sufficient condition for the existence of stochastic robust stabilizing control law are derived. The delay-independent memoryless robust H∞ controllers are constructed to stabilize the given systems in terms of a group of linear matrix inequalities. A numerical simulation example is presented to show that the proposed approach is valid.     

非线性中立型控制系统的鲁棒稳定与鲁棒镇定

研究了一类不确定性的非线性中立型动态系统,系统具有多重时不变状态时滞。其不确定性满足范数有界条件。采用LyapunovV泛函的方法。建立了一类Lyapunov泛函。通过对控制系统(B,D,C)的分析,得出只要矩阵对(B,D)是完全可控的,或者是可稳定的,则在相应的条件下便得出相应的非线性中立型动态控制系统及滞后型动态系统可镇定的充分条件。建立了非线性中立型微分系统的时滞无关的渐近稳定性判别条件,以及非线性中立型动态控制系统的时滞无关鲁棒镇定的判据。同时,给出了相应的非线性滞后微分系统的时滞无关鲁棒稳定性的判据,以及非线性滞后动态控制系统的时滞无关鲁棒镇定性的代数判据。     

Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.     

Adaptive NN stabilization for stochastic systems with discrete and distributed time-varying delays

A new adaptive neural network(NN) output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms.First,an extensional stability notion and the related criterion are introduced.Then,a nonlinear observer to estimate the unmeasurable states is designed,and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability.The effectiveness of the proposed control scheme is demonstrated via a numerical example.     

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.     

连续分布时滞抛物型系统的全局指数稳定性

基于比较原理,利用推广的向量Hanalay微分不等式、Dini导数,结合Green公式及不等式分析技术,研究几类连续分布时滞的抛物型控制系统所导出的滑动模运动方程的全局指数稳定性问题。在仅要求系统的系数矩阵是个M 矩阵的条件下,证明了所获得的滑动模运动方程是全局指数稳定性的,建立了滑动模运动方程全局指数稳定性定理。并为研究连续分布时滞的抛物型系统的变结构控制问题奠定了基础。