基于线性矩阵不等式的网络控制系统设计方法研究

阐述了基于线性矩阵不等式的网络控制系统的设计方法。概述中指出了网络控制系统的不确定模型,并派生出一个充分的稳定条件。基于这一充分条件,提出了一种延迟依赖线性矩阵不等式方法,该方法通过状态反馈控制来稳定网络控制系统。通过实例证明了线性矩阵不等式方法的有效性。     

Fault Estimation for Nonlinear Dynamic Systems

In this paper, the problems of fault detection and estimation for nonlinear dynamic systems are considered by using fault detection observer and adaptive fault diagnosis observer. Based on Lyapunov stability theory and linear matrix inequality (LMI) techniques, a new sufficient condition in terms of LMIs for the proposed problem is derived. At the same time, we get the adaptive fault estimation algorithm. The LMI condition can be easily solved by MATLAB LMI toolbox. Finally, a flexible joint robotic example is given to illustrate the efficiency of the proposed approach.     

Robust Stabilization of Delayed Singular Systems with Linear Fractional Parametric Uncertainties

This paper deals with the problem of robust stabilization for delayed singular systems with parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form involving all system matrices. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are obtained. Moreover, the results generalize and improve previous works on delayed singular systems with norm-bounded parametric uncertainties. A strict linear matrix inequality (LMI) design approach is developed such that, when the LMI is satisfied, a desired robust state feedback control law can be constructed. A numerical example is provided to demonstrate the application of the proposed method.     

Efficient Large-Scale Filter/Filterbank Design via LMI Characterization of Trigonometric Curves

Many filter and filterbank design problems can be posed as the optimization of linear or convex quadratic objectives over trigonometric semi-infinite constraints. Recent advances in design methodology are based on various linear matrix inequality (LMI) characterizations of the semi-infinite constraints, and semidefinite programming (SDP) solutions. Despite these advances, the design of filters of several hundredth order, which typically arise in multicarrier communication and signal compression, cannot be accommodated. This hurdle is due mainly to the large number of additional variables incurred in the LMI characterizations. This paper proposes a novel LMI characterization of the semi-infinite constraints that involves additional variables of miminal dimensions. Consequently, the design of high-order filters required in practical applications can be achieved. Examples of designs of up to 1200-tap filters are presented to verify the viability of the proposed approach.     

H∞ filtering of 2-D discrete systems

This paper deals with H_∞ filtering of two-dimensional (2-D) linear discrete systems described by a 2-D local state-space (LSS) Fornasini-Marchesini (1978) second model. Several versions of the bounded real lemma of the 2-D discrete systems are established. The 2-D bounded real lemma allows us to solve the finite horizon and infinite horizon H_∞ filtering problems using a Riccati difference equation or a Riccati inequality approach. Further a solution to the infinite horizon H_∞ filtering problem based on a linear matrix inequality (LMI) approach is developed. Our results extend existing work for one-dimensional (1-D) systems to the 2-D case and give a state-space solution to the bounded realness of 2-D discrete systems as well as 2-D H_∞ filtering for the first time. Numerical examples are given to demonstrate the Riccati difference equation approach to the 2-D finite horizon H_∞ filtering problem and the LMI approach to the 2-D infinite horizon H_∞ filtering problem     

An FIR Equalizer Design for Nonlinear Channels Using Hybrid GA and LMI

In this paper, a finite impulse response (FIR) equalizer for nonlinear discrete-time channels is designed by employing a hybrid genetic algorithm (GA) and linear matrix inequality (LMI) approach from an H_∞ perspective. The GA technique is utilized to linearize the nonlinear channel model, and the approximate error can be viewed as a state uncertainty. Then, the design of the FIR equalizer is transformed into LMIs, and the coefficients of the FIR equalizer can be obtained by solving an LMI optimization problem. Finally, numerical examples are included to illustrate the effectiveness of the proposed methodology.     

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini–Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.     

Integral-observer-based chaos synchronization

In this paper, a new scheme based on integral observer approach is designed for a class of chaotic systems to achieve synchronization. Unlike the proportional observer approach, the proposed scheme is demonstrated to be effective under a noisy environment in the transmission channel. Based on the Lyapunov stability theory, a sufficient condition for synchronization is derived in the form of a Lyapunov inequality. This Lyapunov inequality is further transformed into a linear matrix inequality (LMI) form by using the Schur theorem and some matrix operation techniques, which can be easily solved by the LMI toolboxes for the design of suitable control gains. It is demonstrated with the Murali-Lakshmanan-Chua system that a better noise suppression and a faster convergence speed can be achieved for chaos synchronization by using this integral observer scheme, as compared with the traditional proportional observer approach.     

Chaotic Synchronization Using Sampled-Data Fuzzy Controller Based on Fuzzy-Model-Based Approach

This paper presents the synchronization of chaotic system using a sampled-data fuzzy controller. To carry out the system analysis, a fuzzy model is employed to represent the chaotic systems. Linear-matrix-inequality (LMI)-based system stability and performance conditions are derived using a Lyapunov-based approach. The derived LMI-based stability and performance conditions are employed to aid the design of a stable and well-performing sampled-data fuzzy controller to achieve the synchronization of chaotic systems. An application example is given to illustrate the merits of the proposed approach.     

Hankel-type model reduction for linear repetitive processes: differential and discrete cases

This paper investigates a Hankel-type model reduction problem for linear repetitive processes. Both differential and discrete cases are considered. For a given stable along the pass process, our attention is focused on the construction of a reduced-order stable along the pass process, which guarantees the corresponding error process to have a specified Hankel-type error performance. The Hankel-type performances are first established for differential and discrete linear repetitive processes, respectively, and the corresponding model reduction problems are solved by using the projection approach. Since these obtained conditions are not expressed in linear matrix inequality (LMI) form, the cone complementary linearization (CCL) method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be solved efficiently. Three numerical examples are provided to demonstrate the proposed theory. This work was partially supported by RGC HKU 7028/04P.     

一类线性不确定切换系统的非脆弱控制器设计

针对一类线性不确定切换系统,利用公共Lyapunov函数的方法,给出了当所设计的控制器存在加性摄动时鲁棒非脆弱控制器存在的条件。该控制器能够保证闭环切换系统在任意切换律下渐近稳定。然后应用线性矩阵不等式将鲁棒非脆弱控制器的设计问题转化为一组线性矩阵不等式的可行解问题,从而可借助Matlab中的LMI工具箱直接求解。最后通过仿真算例验证所提方法的有效性。     

Reliable guaranteed variance filtering against sensor failures

This paper presents a solution to a reliable filtering problem with error variance specifications for both continuous- and discrete-time systems. The filtering error variance in the sensor failure cases is guaranteed to be less than a given upper bound while the performance in the nominal case is optimized. A convergent iterative algorithm based on linear matrix inequality (LMI) is given to obtain the solution. The algorithm solves the problem without introducing additional conservativeness, and it is shown to get better performance and be less conservative compared with traditional LMI approaches. A numerical example is given to show the advantages of our approach over existing techniques.     

An LMI Approach to Optimal Guaranteed Cost Control of Uncertain 2-D Discrete Shift-Delayed Systems via Memory State Feedback

This paper deals with the problem of optimal guaranteed cost control via memory state feedback for a class of two-dimensional (2-D) discrete shift-delayed systems in Fornasini–Marchesini (FM) second model with norm-bounded uncertainties. A new criterion for the existence of memory state feedback guaranteed cost controllers is derived, based on the linear matrix inequality (LMI) approach. Moreover, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controllers which minimize the upper bound of the closed-loop cost function. Illustrative examples demonstrate the merit of the proposed method in the aspect of conservativeness over a previously reported result.     

Impulsive Synchronization of Chaotic Lur'e Systems by Linear Static Measurement Feedback: An LMI Approach

In this brief, we consider impulsive control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems. Impulsive control laws are investigated which make use of linear static measurement feedback, instead of full state feedback. A less conservative sufficient condition than existing results for global asymptotic impulsive synchronization is presented, in which synchronization is proven for the error between the full state vectors. And then an linear matrix inequality (LMI)-based approach for designing linear static output feedback impulsive control laws to globally asymptotically synchronize Lur'e chaotic systems is derived. With the help of the LMI solvers, we can easily obtain the linear output feedback impulsive controller and the bound of the impulsive interval for global asymptotic synchronization. The method is illustrated on Chua's circuit.     

Exponential Stability Analysis for Discrete-Time Singular Systems with Randomly Occurring Delay

This paper investigates the problem of exponential stability analysis for discrete-time singular systems with time-varying delay. The delay enters into the singular systems in a random way, and such randomly occurring delay (ROD) obeys a certain Bernoulli distributed white noise sequence. By employing the linear matrix inequality (LMI) approach, a sufficient condition is established to ensure the considered systems exponentially mean-square stable. Two numerical examples are given to show the usefulness of the obtained result.     

基于H∞控制理论的网络拥塞控制器的设计

针对具有多维性、非线性、动态性、不确定性等复杂特征的计算机网络系统,文章从控制理论出发,提出了一种基于H∞控制理论的主动队列管理（AQM）算法,文章着重分析RED算法。首先,建立了AQM／TCP拥塞控制的动态模型;其次,系统的渐进稳定由线性矩阵不等式（LMI）描述,并应用MATLAB的LMI工具箱求解H∞控制的一般线性时滞系统;然后将求解结果应用到RED中,从而得出了控制器。最后在NS2平台上进行了仿真实验,试验结果表明,该算法在解决系统不确定性引起的鲁棒性问题上是有效的。     

Delay-Dependent Stabilizability of 2D Delayed Continuous Systems with Saturating Control

This paper deals with the problem of stability and stabilization of 2D delayed continuous systems with saturation on the control. An improved delay-dependent stability condition taken from the recent literature is first extended to the case of 2D systems. Second, a delay-dependent stabilizability condition is deduced. The synthesis of stabilizing saturating state feedback controllers for such systems is then given. A set of allowed delays for both directions of the state is computed. All involved conditions are given under LMI formalism. Examples are worked to show the effectiveness of the approach.     

Fast and effective method for low-rank interference suppression inpresence of channel errors

The author presents a simple and computationally effective approach for adaptive spatial interference suppression in the presence of dispersive channel errors. The new method, called lean matrix inversion (LMI), is based on a weighted projection. The corresponding interference subspace is estimated by the transformed columns of the covariance matrix