An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an outputdependent switching law by constructing a robust Luenberger observer for each subsystem.

Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality （LMI） variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

LMI Approach to Mixed H_/H_∞ Fault Detection Observer Design

To investigate the robust fault detection （RFD） observer design for linear uncertain systems, the H_index and H∞ norm are used to describe this observer design as optimization problems. Conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. The solution is obtained by new iterative linear matrix inequality （ILMI） algorithms. The RFD observer design over finite frequency range in which Of does not have full column rank for a system is also considered. Numerical example demonstrates that the designed fault detection observer has high sensitivity to the fault and strong robustness to the unknown input.

LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks

Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).

LMI Approach to Robust H_∞/H_2 Controller Design with Regional Poles Constraint of a Pump-Motor System

The time domain guideposts requirements of a pump-motor system is transfered into a series of constraints which express the robust performance upper bound and regional poles limits of the closed loop system. Then the servo system control problem is transferred into the problem of robust performance optimizing under regional poles constrains described by linear matrix inequality （LMI）. These LMIs are easy to solve through the Matlab LMI-toolbox. Simulations indicate that the controller has excellent dynamic, static and disturbance rejection performance, and the control system is robust and has perfect H2 performance to the bounded external torque disturbance.

An improved constrained model predictive control approach for Hammerstein-Wiener nonlinear systems

Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.

Chaotic Lag Synchronization of Coupled Time-delayed Neural Networks with Two Neurons Using LMI Approach

在这份报纸，混乱落后有二个神经原的联合推迟时间的系统的同步被调查。我们为错误分析 asymptotic 稳定性动态系统基于 Lyapunov 方法和线性矩阵不平等(LMI ) 技术。为决定在联合系统之间的 lag 同步的一些新足够的条件被导出。首先，我们熟练地转移我们第一次以 LMI 被表示进概括特征值最小化编程(GEVP ) 的标准。联合力量的最小成功地被获得。一个数字实验说明我们的结果的有效性和优点。

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.

基于LMI的分段线性系统共存吸引子转迁控制研究

以一类两自由度含间隙分段线性系统为研究对象,利用线性矩阵不等式(linear matrix inequality,LMI)和线性反馈方法对系统共存的吸引子进行在预期目标轨道引导下的转迁控制。在状态平面上利用胞映射方法对系统随参数变化时的共存吸引子进行识别,并基于Poincaré映射和Lyapunov指数研究了系统共存吸引子的稳定性及转迁机理。基于LMI和Lyapunov理论,并利用系统的向量场信息和S-procedure,将系统施加线性反馈控制器后的稳定性和反馈增益矩阵的求解问题转化为LMI描述。利用数值方法验证了所应用的线性反馈控制器及其增益矩阵选取方法的可行性及正确性。

Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions

The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.

LMI_based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.

Robust asymptotic stability for BAM neural networks with time-varying delays via LMI approach

Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.

基于LMI的不确定随机时滞系统输出反馈保性能控制

针对一类范数有界的随机时滞系统,研究在一定性能指标下的保性能控制问题。本文为获得能够实现系统保性能控制的最优输出反馈控制器,采用Lyapunov稳定性理论与LMI技术相结合的方法,将保性能控制问题转化为LMIs约束下的可行解问题。提出的控制器设计方案能够实现系统是依概率全局渐近稳定的,同时满足对系统性能指标的要求。此外,通过数值算例说明所提出控制方案的可行性。