Particle Swarm Optimization for the Design of H∞ Static Output Feedbacks

The design of H∞ reduced order controllers is known to be a non-convex optimization problem for which no generic solution exists. In this paper, the use of Particle Swarm Optimization （PSO） for the computation of H~ static output feedbacks is investigated. Two approaches are tested. In a first part, a probabilistic-type PSO algorithm is defined for the computation of discrete sets of stabilizing static output feedback controllers. This method relies on a technique for random sample generation in a given domain. It is therefore used for computing a suboptimal Ha static output feedback solution, In a second part, the initial optimization problem is solved by PSO, the decision variables being the feedback gains. Results are compared with standard reduced order problem solvers using the COMPIeib （Constraint Matrix-optimization Problem Library） benchmark examples and appear to be much than satisfactory, proving the great potential of PSO techniques.

Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI

This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

Robust H_∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearclled. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function. Then, based on the characterization, a linear matrix inequality （LMI） approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system. A numerical example is presented to demonstrate the application of the proposed method.

Static output feedback stabilization for second-order singular systems using model reduction methods

In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is derived.Then,by using the argument principle,a computable stability criterion is proposed to check the stability of secondorder singular systems.Furthermore,by applying model reduction methods to original systems,a static output feedback design algorithm for stabilizing second-order singular systems is presented.A simulation example is provided to illustrate the effectiveness of the design algorithm.

New synthesis algorithm of static output feedback sliding mode control for a class of uncertain systems

Based on a kind of regular form, a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined sliding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.

H_∞ Output Feedback Control for Stochastic Systems with Mode-dependent Time-varying Delays and Markovian Jump Parameters

This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Markovian jump systems is proposed by constructing an improved Lyapunov-Krasovskii function. Based on this new H∞ disturbance attenuation criterion, a full-order dynamic output feedback controller that ensures the exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Optimal Guaranteed Cost Control via Static Output Feedback for Uncertain Discrete Time Systems

Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods\ An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion\ Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.

Output Feedback Based Admissible Control of Switched Linear Singular Systems

The admissibility analysis and robust admissible control problem of the uncertain discrete-time switched linear singular (SLS) systems for arbitrary switching laws are investigated. Based on linear matrix inequalities, some sufficient conditions are given for: A) the existence of generalized common Lyapunov solution and the admissibility of the SLS systems for arbitrary switching laws, B) the existence of static output feedback control laws ensuring the admissibility of the closed-loop SLS systems for arbitrary switching laws and norm-bounded uncertainties.

Quantized Dynamic Output Feedback H∞ Control for Discrete-time Systems with Quantizer Ranges Consideration

使量子化的动态产量反馈 H 控制为的问题分离时间线性时间不变(LTI ) 系统在这份报纸被调查。考虑的 quantizer 动态、镇静一可调节激增参数和静态的 quantizer。静态的 quantizer 范围具有实际意义并且充分被考虑。首先，考虑量子化错误，使量子化的控制策略控制器状态依赖于不仅而且在系统测量产量上，它被建议以便使量子化的靠近环的系统是 asymptotically 稳定的，与规定 H，性能跳。根据这结果，然后，一个反复的基于 LMI 的优化算法被开发优化静态的 quantizer 范围为靠近环的系统满足 H 表演要求。一个例子被举说明建议方法的有效性。

H∞ Output Feedback Control of Constrained Systems via Moving Horizon Strategy

这份报纸与致动器浸透为分离时间的系统处理 H 产量反馈控制问题。开始，一条抑制 H 输出反馈控制途径在线性矩阵不平等(LMI ) 的框架被介绍优化。在骚乱精力界限上的某些假设下面，靠近环的 H 性能被完成。而且，动人的地平线策略被用于控制性能的一个联机管理以便靠近环的系统能在意外大骚乱的情况中满足控制限制。驱散限制被导出完成动人的地平线靠近环的系统消散。模拟结果证明抑制 H 控制器在骚乱假设下面有效地工作并且动人的地平线 H 控制器罐头交易自动地在令人满意的控制限制和提高的性能之间。

Decentralized robust H-infinity descriptor output feedback control for value-bounded uncertain descriptor large-scale systems

For a class of value-bounded uncertain descriptor large-scale interconnected systems, the decentralized robust H∞ descriptor output feedback control problem is investigated. A design method based on the bounded real lemma is developed for a decentralized descriptor dynamic output feedback controller, which is reduced to a feasibility problem for a nonlinear matrix inequality （NLMI）. It is proposed to solve the NLMI iteratively by the idea of homotopy, where some of the variables are fixed alternately at each iteration to reduce the NLMI to a linear matrix inequality （LMI）. A given example shows the efficiency of this method .

Lipschitz非线性离散系统基于观测器的鲁棒镇定控制设计

本文研究Lipschitz非线性离散时间系统的基于观测器的鲁棒镇定控制问题.首先,针对Lipschitz非线性离散系统,应用微分中值定理和线性参变系统理论,以线性矩阵不等式(LMI)的形式给出基于观测器的鲁棒镇定控制设计的充分条件.随后,将设计结果进一步推广,针对含干扰的Lipschitz非线性离散系统进行H∞性能分析,实现了基于观测器的鲁棒H∞镇定控制,同时给出观测器增益矩阵和控制器增益矩阵的一步求解算法.最后,通过两个数值例子验证了所提方法的有效性.

Fuzzy Robust H1 Control for UncertainNonlinear Systems via Output Feedback

This paper is concerned with a fuzzy robust H∞ control problem via output feedbackfor a class of uncertain nonlinear systems. The uncertain nonlinear systemsare represented by fuzzy Takagi-Sugeno （T-S） model, and a fuzzy controller is designedbased on the state observer. A sufficient condition for the existence of fuzzycontroller is given in terms of the linear matrix inequalities （LMIs） and the adaptivelaw. Based on Lyapunov stability theorem, the proposed fuzzy control scheme suchthat the desired H∞performance is achieved in the sense that all the closed-loopsignals are uniformly ultimately bounded （UUB）. Simulation results indicate theeffectiveness of the developed control scheme. In this paper, a less conservativefuzzy tracking controller is proposed, where the matching condition and the upperbound are avoided. Comparing with the existing works, the dimension of the LMIsof this paper is reduced.

Output Feedback Controller Design for Discrete-time Switched Singular Systems

This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The objective is to design a suitable robust SOF controller guaranteeing the regularity,causality and asymptotic stability of the resulting closed-loop system under arbitrary switching laws. Based on the basic matrix inequality sufficient condition for checking the admissibility of switched singular systems,together with some matrix inequality convexifying techniques,the SOF controller synthesis is developed for the underlying systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities( LMIs). A simulation example is given to show the effectiveness of the proposed method.

H_2 Output Feedback Control for Airborne Dispenser Uncertain Generalized System

The problem of H2 output feedback control for generalized system with structural uncertainties is studied using linear matrix inequality approach. A sufficient condition Of linear matrix inequality is presented such that the closed-loop system is stable and satisfies H2 performance for all admissible uncertainties. Furthermore, the solution of the controller is given. An H2 output feedback controller is designed in the airborne dispenser pitch channel, and the simulation results show that the controller is effective.

H-infinity output feedback control for descriptor systems with delayed states

This paper considers the H-infinity dynamic output feedback control for descriptor systems with delay in states. The controller is a descriptor system without delay. Several equivalent sufficient conditions for the existence of one descriptor dynamic controller without impulsive models are given. Furthermore the explicit expression of the desired controller is obtained. The detailed design of the controller is presented using the cone complementarity linearization iterative algorithm and the LMI method. A ntumerical example is shown to illustrate the designed method.

基于线性矩阵不等式的环形永磁力矩电机的H_2/H_∞静态输出反馈控制

针对直接驱动数控转台用环形永磁力矩电机易受负载扰动及自身参数变化影响的特点,文中基于线性矩阵不等式(linear matrix inequality,LMI),设计了一个多目标混合H2/H∞静态输出反馈控制器,该控制器可使闭环系统的极点均落在预先选定的线性矩阵不等式区域D内来实现极点配置。所设计的多目标控制器同时考虑了闭环系统的极点位置和2个重要的鲁棒性能指标(H2和H∞范数),不但保证系统的稳定型和快速性,还使系统对外界及自身扰动具有较强的鲁棒性,在很大程度上解决快速性和鲁棒性之间的矛盾。仿真结果及分析表明,所提出控制器满足高精度直接驱动数控转台用环形永磁力矩电机伺服系统对快速性和鲁棒性的要求。