STABILITY ANALYSIS OF UNCERTAIN DISCRETE‐TIME SYSTEMS WITH TIME‐VARYING STATE DELAY: A PARAMETER‐DEPENDENT LYAPUNOV FUNCTION APPROACH

This paper presents several new robust stability conditions for linear discrete‐time systems with polytopic parameter uncertainties and time‐varying delay in the state. These stability criteria, derived by defining parameter‐dependent Lyapunov functions, are not only dependent on the maximum and minimum delay bounds, but also dependent on uncertain parameters in the sense that different Lyapunov functions are used for the entire uncertainty domain. It is established, theoretically, that these robust stability criteria for the nominal and constant‐delay case encompass some existing result as their special case. The delay‐dependent and parameter‐dependent nature of these results guarantees the proposed robust stability criteria to be potentially less conservative.     

一种时滞连续系统零极点辨识算法

１前言在工程应用中,相当一部分工业过程可由带有实零极点及时滞的传递函数描述,一些典型的控制算法也是基于系统的实零极点进行设计的［１—３］．虽然我们可通过对分子、分母多项式构成的传递函数进行因式分解间接求得过程的零极点,但在实时辨识中却很难做到求得的零...     

STATE FEEDBACK CONTROLLER DESIGN OF NETWORKED CONTROL SYSTEMS WITH PARAMETER UNCERTAINTY AND STATE‐DELAY

This paper is concerned with the controller design of networked control systems. The continuous time plant with parameter uncertainty and state delay is studies. A new model of the networked control system is provided under consideration of the nonideal network conditions. In terms of the given model, a controller design method is proposed based on a delay dependent approach. The maximum allowable synthetical bounds related with the discarded data packet and network‐included delay and the feedback gain of a memoryless controller can be derived by solving a set of linear matrix inequalities for the stabilizablity of the networked control system based on Lyapunov functional method. An example is given to show the effectiveness of our method.     

ON ROBUST STABILITY OF LINEAR NEUTRAL SYSTEMS WITH MIXED DELAYS AND NORM‐BOUNDED UNCERTAINTY

This paper investigates the robust stability of linear neutral systems with mixed delays and norm‐bounded uncertainty. Using new Lyapunov‐Krasovskii functionals, less conservative delay‐dependent robust stability conditions for such systems in terms of linear matrix inequalities (LMIs) are derived. Numerical examples show that the results obtained in this paper significantly improve the estimate of the stability limit over some existing results in other literature.     

ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME‐VARYING DELAYS

This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time‐varying delays. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The purpose of the robust stabilization problem is to design a feedback control law such that the resulting closed‐loop system is robustly stable. This problem is solved via generalized quadratic stability approach. A strict linear matrix inequality (LMI) design approach is developed. Finally, a numerical example is provided to demonstrate the application of the proposed method.     

DISCRETIZING CONTINUOUS‐TIME CONTROLLERS WITH FUZZY LOGIC SYSTEMS AND ITS STABILITY ANALYSIS

In this paper, a new method, applying the fuzzy logic system, is proposed to discretize the continuous‐time controller in computer‐controlled systems. All the continuous‐time controllers can be reconstructed by the proposed method under the Sampling Theorem. That is, the fuzzy logic systems are used to add nonlinearity and to approximate smooth functions. Hence, the proposed controller is a new smooth controller that can replace the original controller, independent of the sampling time under the Sampling Theorem. Consequently, the proposed controller not only can discretize the continuous‐time controllers, but also can tolerate a wider range of sampling time uncertainty. Besides, the input‐output stability is proposed for discretizing the continuous‐time controller of the fuzzy logic systems. Finally, computer simulation shows that the proposed method can easily reconstructthe continuous‐time controller and has very good robustness for different sampling times.     

SIMPLE INSTABILITY CRITERION FOR A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME DELAYS

In this paper, the instability for a class of singular systems with discrete and distributed time delays is investigated. Simple instability criterion, which is a delay‐dependent criterion, is derived to guarantee the instability of such systems. Finally, a numerical example is given to illustrate the use of the main result.     

MULTI‐HOPPING INDUCED GAIN SCHEDULING FOR WIRELESS NETWORKED CONTROLLED SYSTEMS

A multi‐hopping induced gain scheduler for Wireless Networked Controlled Systems (WiNCS) is proposed. The control scheme is based on a client‐server architecture. The data packets are assumed to be carried over a network composed of wireless sensor nodes running the 802.11b protocol. The number of hops necessary for packets to reach their destinations is variable and depends on current traffic conditions. Changes in the number of hops induces changes in the latency times introduced by the communication network in the feedback loop. To deal with these changes an LQR‐output feedback scheme is introduced, whose parameters are adjusted according to the number of the hops. The weights of the LQR controllers are subsequently tuned using LMIs to ensure a prescribed stability margin despite the variable latency times. The overall scheme resembles a gain scheduled controller with the number of hops playing the role of the scheduling parameter. Simulation results on the NS‐2 simulator are provided to highlight the efficacy of the proposed scheme.     

SENSITIVITY APPROACH TO OPTIMAL CONTROL FOR AFFINE NONLINEAR DISCRETE‐TIME SYSTEMS

This paper deals with the optimal control problem for a class of affine nonlinear discrete‐time systems. By introducing a sensitivity parameter and expanding the system variables into a Maclaurin series around it, we transform the original optimal control problem for affine nonlinear discrete‐time systems into the optimal control problem for a sequence of linear discrete‐time systems. The optimal control law consists of an accurate linear term and a nonlinear compensating term, which is an infinite sequence of adjoint vectors. In the present approach, iteration is required only for the nonlinear compensation series. By intercepting a finite sum of the series, we obtain a suboptimal control law that reduces the complexity of the calculations. A numerical simulation shows that the algorithm can be easily implemented and has a fast convergence rate.     

STOCHASTIC STABILIZATION AND H∞ CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS

In this paper, robust stochastic stabilization and H_∞ control for a class of uncertain discrete‐time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state‐feedback controller design procedure for discrete time‐delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H_∞ control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results.     

FINITE TIME STABILITY ANALYSIS OF LINEAR AUTONOMOUS FRACTIONAL ORDER SYSTEMS WITH DELAYED STATE

For the first time, in this paper, a stability test procedure is proposed for linear time‐invariant fractional order systems (LTI FOS). Paper extends some basic results from the area of finite time and practical stability to linear, continuous, fractional order time invariant time‐delay systems given in state space form. Sufficient conditions of this kind of stability, for particular class of fractional time‐delay systems is derived.     

ADAPTIVE DYNAMIC MATRIX CONTROL FOR NETWORK‐BASED CONTROL SYSTEMS WITH RANDOM DELAYS

Random transfer delays in network‐based control systems (NCSs) degrade the control performance and can even destabilize the control system. To address this problem, the adaptive dynamic matrix control (DMC) algorithm is proposed. The control algorithm is derived by applying the philosophy behind DMC to a discrete time‐delay model. A method to estimate the network‐induced delays is also presented to facilitate implementation of the control algorithm. Finally, an NCS platform based on the TrueTime simulator is constructed. With it, the adaptive DMC algorithm is compared with the conventional DMC algorithm under different network conditions. Simulation results show that the proposed adaptive DMC algorithm can respond to various network conditions adaptively and achieve better control performance for NCSs with random transfer delays.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE‐TIME SINGULAR SYSTEMS WITH TIME‐DELAY AND NONLINEAR PERTURBATION

This paper discusses a generalized quadratic stabilization problem for a class of discrete‐time singular systems with time‐delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S‐procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete‐time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non‐singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples.     

具有状态和控制滞后不确定系统的保性能控制器设计

1　引言本文的目的在于将文献 [1 ]的结论推广到同时具有状态和控制滞后的不确定系统 ,并进而研究其最优保性能控制问题 .考虑具有状态和控制滞后的不确定系统x( t) =[A DF( t) E1 ] x( t) [Ad DF( t) Ed] x( t-d) [B DF( t) E2 ] u( t) [Bh DF( t) Eh]《u》( t-     

网络控制系统的分析与建模

本文论述了网络控制系统的复杂性及当前网络控制系统建模中存在的主要缺点. 在考虑系统噪声、控制器动态及输出反馈的情况下，提出了多包传输、单包传输有数据包丢 失及多包传输有数据包丢失时网络控制系统的离散随机模型的统一的建模方法，并给出了网 络诱导时延合并定理．     

ROBUST H∞ CONTROL AND QUADRATIC STABILIZATION OF DISCRETE‐TIME SWITCHED SYSTEMS WITH NORM‐BOUNDED TIME‐VARYING UNCERTAINTIES

We focus on robust H_∞ control analysis and synthesis for discretetime switched systems with norm‐bounded time‐varying uncertainties. Sufficient conditions are derived to guarantee quadratic stability along with a prescribed H_∞‐norm bound. Each of them can be dealt with as a linear matrix inequality (LMI) which can be tested with efficient algorithms. All the switching rules are constructively designed, and do not rely on any uncertainties.     

多组多滞后区间系数时变非线性关联控制系统的结构与关联鲁棒镇定（Ⅰ）

建立了多组多滞后区间系数时变非线性控制系统的结构概念，采用刘永清建立的鲁棒镇定的等价法，给出了具有扰动结构参数的多组多滞后区间系数时变非线性关联控制系统的结构与关联鲁棒镇定，同时给出了扰动参数与滞后非线性项界限的估计公式