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.

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.

MATLAB LMI工具在鲁棒稳定性分析中的应用

针对一类普遍存在的不确定时滞系统,基于线性矩阵不等式(LMI)的描述进行系统的稳定性分析,得到了用一个线性矩阵不等式系统的可行性表示的鲁棒稳定性滞后依赖型条件。介绍了如何利用MATLAB软件中的LMI工具箱进行分析与设计,据此计算出最大的允许时滞界。针对此类系统的鲁棒稳定性分析给出了数值算例。

Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality （LMI） approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed- loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.

Robust stabilization of switched discrete-time systems with actuator saturation

This paper studies the robust stabilization problem of switched discrete-time linear systems subject to actuator saturation. New switched saturation-dependent Lyapunov functions are exploited to design a robust stabilizing state feedback controller that maximizes an estimation of the domain of attraction. The design problem of controller （coefficient matrices） is then reduced to an optimization problem with linear matrix inequality （LMI） constraints. A numerical example is given to show the effectiveness of the proposed method.

Robust decentralized H_∞ control of multi-channel systems with norm-bounded parametric uncertainties

A robust decentralized H∞ control problem for uncertain multi-channel systems is considered. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. The dynamic output feedback is mainly dealt with. A necessary and sufficient condition for the uncertain multi-channel system to be stabilized robustly with a specified disturbance attenuation level is derived based on the bounded real lemma, which is reduced to a feasibility problem of a nonlinear matrix inequality （NMI）. A two-stage homotopy method is used to solve the NMI iteratively. First, a decentralized controller for the nominal system with no uncertainty is computed by imposing structural constraints on the coefficient matrices of the controller gradually. Then the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, a variable is fixed alternately at the iterations to reduce the NMI to a linear matrix inequality （LMI）. A given example shows the efficiency of this method.

Delay-dependent robust stabilization for a class ofneutral systems with nonlinear perturbations

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities （LMI）. Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

Input-output approach to robust stability and stabilization for uncertain singular systems with time-varying discrete and distributed delays

Based on input-output approach, the robust stability and stabilization problems for uncertain singular systems with time-varying delays are investigated. The parameter uncertainties are assumed to be norm-bounded and the time-varying delays include both discrete delay and distributed delay. By introducing a new input-output model, the time-delay system is embedded in a family of systems with a forward system without time delay and a dynamical feedback uncertainty. A sufficient and necessary condition, which guarantees the system regular, impulse-free and stable for all admissible uncertainties, is obtained. Based on the strict linear matrix inequality, the desired robust state feedback controller is also obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.

New delay-dependent robust stability and stabilization for uncertain T-S fuzzy time-delay systems under imperfect premise matching

To alleviate the conservativeness of the stability criterion for Takagi-Sugeno(T-S)fuzzy time-delay systems,a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term,which was firstly used to derive the stability criterion for T-S fuzzy time-delay systems.By the same approach,the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered.On the other hand,in order to enhance the design flexibility,a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed,which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model.By the numerical examples,the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains.For instance,when the allowable time-delay increases from 7.3s to 12s for an uncertain T-S fuzzy control system with time-delay,the norm of the feedback gains decreases from(34.299 2,38.560 3)to(10.073 3,11.349 0),respectively.Meanwhile,the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition ofx(0)=[3-1].

Robust stabilization and disturbance attenuation for a class of underactuated mechanical systems

The robust control problem for a class of underactuated mechanical systems called acrobots is addressed.The goal is to drive the acrobots away from the straight-down position and balance them at the straight-up unstable equilibrium position in the presence of parametric uncertainties and external disturbance.First,in the swing-up area,it is shown that the time derivative of energy is independent of the parameter uncertainties,but exogenous disturbance may destroy the characteristic of increase in mechanical energy.So,a swing-up controller with compensator is designed to suppress the influence of the disturbance.Then,in the attractive area,the control problem is formulated into a H∞ control framework by introducing a proper error signal,and a sufficient condition of the existence of H∞ state feedback control law based on linear matrix inequality(LMI) is proposed to guarantee the quadratic stability of the control system.Finally,the simulation results show that the proposed control approach can simultaneously handle a maximum ±10% parameter perturbation and a big disturbance simultaneously.

Design of decentralized robust stabilizing controller for interconnected time-varying uncertain systems

For interconnected uncertain systems which are time-varying and assumed to satisfy the matching conditions, a sufficient condition for decentralized stabilization feedback control laws is derived. This condition is expressed as the solvability problem of linear matrix inequalities (LMIs). Based on that, a convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design a decentralized state feedback controI with smaller gain parameters which enables the closed-loop system asymptotically stable.

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.

LMI conditions for quadratic and robust D-stability of interval systems

Sufficient conditions for the quadratic D-stability and further robust D-stability of interval systems are presented in this paper. This robust D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities （LMIs） defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as in previous results. The results contain the usual quadratic and robust stability of continuous-time and discrete-time interval systems as particular cases. The illustrative example shows that this method is effective and less conservative for checking the quadratic and robust D-stability of interval systems.

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.

Robust D stabilization of singular systems with polytopic uncertainties

The robust D stabilization problem is considered for singular systems with polytopic uncertainties in this paper.Both the derivative matrix E and the state matrix A are with uncertainties,which were not considered before.First,with the introduction of some free matrices,a necessary and sufficient condition for the singular system to be D stable is proposed,based on which,the robust D stable problem is solved,and a sufficient condition for the closed system to be robust D stabilizable is obtained.The desired state feedback controller is given in an explicit expression.Numerical examples show the efficiency of the proposed approach.

基于LMI的μ方法及其在电力系统中的应用

对现有基于线性矩阵不等式(LMI)的m (结构奇异值,SSV)方法进行了优化,给出了基于大规模稀疏LMI算法的m鲁棒控制器设计算法,并将m方法应用于SMIB系统励磁控制的鲁棒稳定性分析和鲁棒控制器的设计,将其结果同经典的PSS控制器的结果做了比较。数值结果表明,所得m控制器在追踪控制能力和鲁棒性等方面优于传统的AVR+PSS控制方式。

参数不确定性关联大系统的分散鲁棒镇定的LMI方法

考虑了一类参数不确定性关联大系统的分散鲁棒镇定问题.所考虑的不确定性参数满足范数有界条件.利用LMI技术,基于Lyapunov稳定性理论给出了保证该不确定关联大系统闭环渐近稳定的充分条件.并给出数值例子说明了该条件的应用.

具有不匹配互联项相似组合大系统的分散控制及输出跟踪的LMI方法

研究一类相似组合大系统 ,其互联项不满足匹配条件。提出一种新的分散控制器设计方法 ,并结合线性矩阵不等式方法给出了系统渐近稳定的充分条件 ,其结果由 N个线性矩阵不等式给出。用此方法研究了输出跟踪问题 ,并用仿真例子说明了该方法的有效性。

带有外干扰的滞后离散广义系统鲁棒H_∞控制器设计:LMI方法

研究了带有外部干扰与状态滞后的离散广义系统鲁棒控制器的设计问题 .在对系统进行稳定分析的基础上 ,给出了系统可以鲁棒镇定的条件 ,并且将这一条件表示为线性矩阵不等式 (LMI)的形式 ,从而使得控制器的设计问题可利用现有的LMI方法解决 .