时滞线性区间系统的鲁棒稳定与鲁棒镇定

利用一个微分不等式给出了几类具有区间 系数的时滞系统的鲁棒稳定和鲁棒镇定的充分条件,这些条件只需判断一个常数矩阵是否为 M矩阵,使用方便．     

IMPROVED CONDITIONS FOR DELAY‐DEPENDENT ROBUST STABILITY AND STABILIZATION OF UNCERTAIN DISCRETE TIME‐DELAY SYSTEMS

This paper provides improved delay‐dependent conditions for the robust stability and robust stabilization of discrete time‐delay systems with norm‐bounded parameter uncertainties. It is theoretically established that the proposed conditions are less conservative than those discussed in the literature. The new approach proposed in this paper in a derivation of delay‐dependent conditions and involves the use of neither model transformation nor bounding techniques for some cross terms. A numerical example is provided to demonstrate the reduced conservatism of the proposed conditions.     

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.     

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.     

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.     

DESIGN MODIFICATION OF SLIDING MODE OBSERVERS FOR UNCERTAIN MIMO SYSTEMS WITHOUT AND WITH TIME‐DELAY

In this paper, the sliding mode observers design techniques for MIMO and as a simple example for SISO systems are systematically advanced as a first purpose. Design parameters are selected such that on the defined switching surface always is generated asymptotically stable sliding mode. Moreover, observer state error dynamics is globally robustly asymptotically stable. Then, advanced design techniques are generalized to the design of a new modification of sliding mode observers for uncertain MIMO systems with time‐delay. Robust sliding and global asymptotic stability conditions are derived by using Lyapunov‐Krasovskii V‐functional method. By these conditions observer parameters are designed such that an asymptotically stable sliding mode always is generated in observer and observer state error dynamics is robustly globally asymptotically stable. The main results are formulated in terms of Lyapunov matrix equations and inequalities. Design example for AV‐8A Harrier VTOL aircraft with simulation results using MATLAB‐Simulink show the effectiveness of proposed design approaches.     

ADAPTIVE ROBUST CONTROL OF UNCERTAIN SYSTEMS WITH TIME‐VARYING STATE DELAY

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time‐varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time‐delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.     

A NEW LMI CONDITION FOR DELAY‐DEPENDENT ROBUST STABILITY OF STOCHASTIC TIME‐DELAY SYSTEMS

This paper studies robust stability for a class of uncertain nonlinear stochastic time‐delay systems. In terms of a linear matrix inequality, an improved delay‐dependent condition guaranteeing that a stochastic delay system will be exponentially stable in the mean square is proposed. This condition is less conservative than existing ones in the literature and is demonstrated by means of an example.     

ROBUST OUTPUT FEEDBACK GUARANTEED COST CONTROL FOR 2‐D UNCERTAIN STATE‐DELAYED SYSTEMS

This paper considers the robust guaranteed cost control problem of two‐dimensional (2‐D) state‐delayed systems. First, the definition of guaranteed cost matrix is proposed and an upper bound of the cost function is given. Then, the guaranteed cost control problem is resolved. Furthermore, the minimum upper bound of the closed‐loop cost function is obtained by solving an optimization problem with LMIs' constraints. A numerical example demonstrates the effectiveness of our results.     

AN LMI APPROACH TO ROBUST STABILITY OF UNCERTAIN DISCRETE SINGULAR TIME‐DELAY SYSTEMS

The problem of robust stability analysis for uncertain discrete singular time‐delay systems is investigated in this paper. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time‐delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncertain discrete singular time‐delay system. Two numerical examples are provided to demonstrate the feasibility of the proposed approach.     

ROBUST CONTROL FOR A CLASS OF UNCERTAIN STATE‐DELAYED SINGULARLY PERTURBED SYSTEMS

This paper considers the problem of robust control for a class of uncertain state‐delayed singularly perturbed systems with norm‐bounded nonlinear uncertainties. The system under consideration involves state time‐delay and norm‐bounded nonlinear uncertainties in the slow state variable. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed‐loop system for all ∞ ∞ (0, ∞00) and independently of the time‐delay. Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed. We present an illustrative example to demonstrate the applicability of the proposed design approach.     

H2‐OPTIMAL SAMPLED‐DATA CONTROL FOR PLANTS WITH MULTIPLE INPUT AND OUTPUT DELAYS

The sampled‐data H₂‐optimization problem for plants with multiple input and output delays is considered. An equivalent discrete‐time system is constructed and numerical algorithm for computing matrices of its state‐space realization is presented. It is proved that stability of this system is equivalent to stability of original sampled‐data system. The proposed method can be applied to a wide class of digital control problems for continuous‐time plants with multiple input and output delays.     

A NEW DESIGN APPROACH TO DELAY‐DEPENDENT ROBUST H∞ CONTROL FOR UNCERTAIN TIME‐DELAY SYSTEMS

A new design approach to delay‐dependent robust stabilization and robust H∞ control for a class of uncertain time‐delay systems is provided in this paper. The sufficient conditions for delay‐dependent robust stabilization and robust H∞ control are derived based on a new state transformation and given in terms of linear matrix inequalities (LMI). Numerical examples are presented to show that the proposed results can be less conservative and can be used to deal with not only small but also large delay systems.     

Necessary and Sufficient Stability Criterion and Stabilization for Positive 2‐D Continuous‐Time Systems with Multiple Delays

This paper addresses the stability and control problem of the linear positive two‐dimensional (2‐D) continuous‐time systems in Roesser model with multiple time delays. The contribution lies in two aspects. First, a simple novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for 2‐D continuous delayed systems. It turns out that the magnitude of delays has no any impact on the stability of these systems, which is completely determined by the system matrices. Second, a necessary and sufficient condition for the existence of state‐feedback controllers is proposed for general delayed 2‐D systems, which ensures the non‐negativity and the stability of the resulting closed‐loop systems. Two examples are given to validate the proposed methods.     

Delay‐dependent Stability and Static Output Feedback Control of 2‐D Discrete Systems with Interval Time‐varying Delays

This paper is concerned with the problems of delay‐dependent stability and static output feedback (SOF) control of two‐dimensional (2‐D) discrete systems with interval time‐varying delays, which are described by the Fornasini‐Marchesini (FM) second model. The upper and lower bounds of delays are considered. Applying a new method of estimating the upper bound on the difference of Lyapunov function that does not ignore any terms, a new delay‐dependent stability criteria based on linear matrix inequalities (LMIs) is derived. Then, given the lower bounds of time‐varying delays, the maximum upper bounds in the above LMIs are obtained through computing a convex optimization problem. Based on the stability criteria, the SOF control problem is formulated in terms of a bilinear matrix inequality (BMI). With the use of the slack variable technique, a sufficient LMI condition is proposed for the BMI. Moreover, the SOF gain can be solved by LMIs. Numerical examples show the effectiveness and advantages of our results.     

Exponential stabilization of uncertain time‐delay linear systems with Markovian jumping parameters

This paper studies the exponential stabilization problem of uncertain time‐delay linear systems with Markovian jumping parameters. A novel delay decomposition approach is developed to derive delay‐dependent conditions under which the closed‐loop control system is mean square exponentially stable for all admissible uncertainties. It is shown that the feedback gain matrices and the decay rate can be obtained by solving coupled linear matrix inequalities. Moreover, the difficulties arising from searching for tuning parameters in the existing methods are overcome. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

OPTIMAL REJECTION WITH ZERO STEADY‐STATE ERROR OF SINUSOIDAL DISTURBANCES FOR TIME‐DELAY SYSTEMS

This paper studies the problem of optimal rejection with zero steady‐state error of sinusoidal disturbances for linear systems with time‐delay. Based on the internal model principle, a disturbance compensator is constructed to counterbalance the external sinusoidal disturbances, so that the original system can be transformed into an augmented system without disturbances. Then, with the introduction of a sensitivity parameter and expanding power series around it, the optimal disturbance rejection problem can be simplified to the problem of solving an infinite sum of a linear optimal control series without time‐delay or disturbance. The optimal control law for disturbance rejection with zero steady‐state error consists of accurate linear state feedback terms and a time‐delay compensating term, which is an infinite sum of an adjoint vector series. In the presented approach, iteration is required only for the time‐delay compensation series. By intercepting a finite sum of the compensation series, we obtain an approximate physically realizable optimal control law that avoids complex calculation. A numerical simulation shows that the algorithm is effective and easy to implement.     

Robust stabilization of nonlinear stochastic 2‐D systems: LaSalle‐type theorem approach

LaSalle theorem (also known as the LaSalle invariance principle) plays an essential role in the systems and control theory. Recently, it has been extensively studied and developed for various types of one‐dimensional (1‐D) systems including deterministic and stochastic 1‐D systems in discrete‐ and continuous‐time domains. For two‐dimensional (2‐D) systems, such studies have received considerably less attention. In this article, based on discrete martingale theory, a LaSalle‐type theorem is first developed for a class of discrete‐time nonlinear stochastic 2‐D systems described by a Roesser model. The proposed result can be regarded as an extension of stochastic Lyapunov‐like theorem, which guarantees the convergence almost surely of system state trajectories. Extensions to the problem of optimal guaranteed cost control of nonlinear stochastic 2‐D systems are also presented. The proposed schemes are then utilized to derive tractable synthesis conditions of a suboptimal state‐feedback controller for uncertain 2‐D systems with multiplicative stochastic noises. The effectiveness of the obtained results is illustrated by given numerical examples and simulations.     

Observer‐based tracking control for switched stochastic systems based on a hybrid 2‐D model

This paper is concerned with the observer‐based output tracking problem for a class of linear switched stochastic systems with time delay and disturbance by using repetitive control approach. More precisely, a two‐dimensional hybrid model is incorporated to obtain and optimize the repetitive controller. In particular, the repetitive controller is used to improve the tracking performance through its continuous learning actions. In addition, an equivalent‐input‐disturbance estimator is incorporated into the repetitive control design approach to reduce the effect of the external disturbances. The main aim of the control design is to track the periodic reference signal with the measured output of the system under consideration even in the presence of an unknown bounded disturbance. By constructing a suitable Lyapunov‐Krasovskii functional and using average dwell time approach and Jensen inequality, sufficient conditions are obtained in terms of linear matrix inequalities to guarantee the mean‐square exponential stability of the considered system. Eventually, a numerical example is provided to demonstrate the effectiveness of the developed method.     

Quantized Iterative Learning Control Design For Linear Systems Based On A 2‐D Roesser Model

This paper considers the problem of iterative learning control design for linear systems with data quantization. It is assumed that the control input update signals are quantized before they are transmitted to the iterative learning controller. A logarithmic quantizer is used to decode the signal with a number of quantization levels. Then, a 2‐D Roesser model is established to describe the entire dynamics of the iterative learning control (ILC) system. By using the sector bound method, a sufficient asymptotic stability condition for such a 2‐D system is established and then the ILC design is given simultaneously. The result is also extended to more general cases where the system matrices contain uncertain parameters. The effectiveness of the proposed method is illustrated by a numerical example.