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一类线性离散时间系统有限时间控制问题 总被引:4,自引:2,他引:2
讨论一类具有时变、有限能量外部扰动的线性离散时间系统的有限时间控制问题.首先研究问题可解的充分条件,并讨论了状态反馈控制器存在的条件,这些条件可归结为基于线性矩阵不等式(LMI)的可解性问题;然后给出状态反馈控制器和输出反馈控制器的具体设计;最后通过仿真验证了该方案的有效性. 相似文献
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针对一类线性系统,研究了基于H∞的鲁棒PID控制器的设计方法,使得闭环系统的所有极点均位于一个给定的LMI区域中.采用线性矩阵不等式的处理方法,证明了该问题等价于一组线性矩阵不等式的可解性问题.利用该线性矩阵不等式的可行解给出了PID控制器的构造方法,并通过现有的软件Matlab中的工具箱LMI来进行求解.该方法很好地解决了PID控制下的极点指标和H∞鲁棒控制的相容性问题.实际的工程算例验证了该方法的有效性和可行性. 相似文献
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讨论一类具有有限能量的外部扰动的线性离散广义系统的有限时间控制问题。分析问题可解性,得到该问题可解的充分条件,通过状态反馈控制器和输出反馈控制器的设计,给出实现闭环系统有限时间有界的充分条件,这些充分条件可以转化为线性矩阵不等式(LMI)的可行解问题,可借助Matlab中的LMI工具箱求解,最后通过数值算例验证该方法的... 相似文献
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利用李雅谱诺夫稳定理论及线性矩阵不等式(LMI)方法, 研究了具有非结构摄动的不确定连续系统经动态输出反馈的二次鲁棒能稳定问题. 推导出这类控制器存在的充分条件, 即一个拟线性矩阵不等式(Q-LMI)的形式, 给出了Q-LMI问题的基于LMI方法的求解步骤. 为了使得Q-LMI问题有解, 可引入一些LMI约束, 提高了Q-LMI问题的可解性. 基于Q-LMI条件, 揭示了系统不确定参数界与系统控制规模的关系, 提出了“不同的摄动实施不同规模的控制”的鲁棒能稳定的分层次控制策略. 最后, 通过一个例子说明了 相似文献
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线性分式不确定系统保成本控制及其鲁棒界 总被引:1,自引:0,他引:1
研究线性分式不确定系统的动态输出反馈保成本控制.采用线性矩阵不等式(LMI)方法证明了保成本控制器存在的充分必要条件等价于一个LMI可解性问题,通过该条件将求解闭环系统的成本函数上界的最小值问题转化为一个凸优化问题,利用该凸优化问题的解,得到动态输出反馈控制器的增益矩阵,并且给出了摄动参数允许最大摄动界的一种算法. 相似文献
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This paper is concerned with the problem of robust output feedback controller design for a class of linear discrete‐time systems with normbounded uncertainty. The objective is to design a controller such that the closed‐loop poles are assigned within a specified disc and the steady regulated output covariance is guaranteed to be less than a given upper bound. Using a linear matrix inequality (LMI) approach, the existence conditions of such controllers are derived, and a parametrized characterization of a set of desired controllers (if they exist) is presented in terms of the feasible solutions to a set of LMIs. A procedure is given to select a suitable output feedback controller that minimizes the desired control effort. 相似文献
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This paper studies the non‐fragile Guaranteed Cost Control (GCC) problem via memoryless state‐feedback controllers for a class of uncertain discrete time‐delay linear systems. The systems are assumed to have norm‐bounded, time‐varying parameter uncertainties in the state, delay‐state, input, delay‐input and state‐feedback gain matrices. Existence of the guaranteed cost controllers are related to solutions of some linear matrix inequalities (LMIs). The non‐fragile GCC state‐feedback controllers are designed based on a convex optimization problem with LMI constraints to minimize the guaranteed cost of the resultant closed‐loop systems. Numerical examples are given to illustrate the design methods. 相似文献
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A new approach for design of robust decentralized controllers for continuous linear time‐invariant systems is proposed using linear matrix inequalities (LMIs). The proposed method is based on closed‐loop diagonal dominance. Sufficient conditions for closed‐loop stability and closed‐loop block‐diagonal dominance are obtained. Satisfying the obtained conditions is formulated as an optimization problem with a system of LMI constraints. By adding an extra LMI constraint to the system of LMI constraints in the optimization problem, the robust control is addressed as well. Accordingly, the decentralized robust control problem for a multivariable system is reduced to an optimization problem for a system of LMI constraints to be feasible. An example is given to show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Guang-Hong Yang Jiuxiang Dong 《Fuzzy Systems, IEEE Transactions on》2008,16(3):615-629
This paper considers the problem of designing stabilizing and Hinfin controllers for nonlinear singularly perturbed systems described by Takagi-Sugeno fuzzy models with the consideration of the bound of singular perturbation parameter e. For the synthesis problem of simultaneously designing the bound of e and stabilizing or Hinfin controllers, linear matrix inequalities (LMI)- based methods are presented. For evaluating the upper bound of e subject to stability or a prescribed Hinfin performance bound constraint for the resulting closed-loop system, sufficient conditions are developed, respectively. For the stabilizing and Hinfin control synthesis without the consideration of improving the bound of e, new design methods are also given in terms of solutions to a set of LMIs. Examples are given to illustrate the efficiency of the proposed methods. 相似文献
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This paper proposes a unified approach to linear controller synthesis that employs various LMI conditions to represent control specifications. We define a comprehensive class of LMIs and consider a general synthesis problem described by any LMI of the class. We show a procedure that reduces the synthesis problem, which is a BMI problem, to solving a certain LMI. The derived LMI condition is equivalent to the original BMI condition and also gives a convex parametrization of all the controllers that solve the synthesis problem. The class contains many of widely-known LMIs (for H∞ norm, H2 norm, etc.), and hence the solution of this paper unifies design methods that have been proposed depending on each LMI. Further, the class also provides LMIs for multi-objective performance measures, which enable a new formulation of controller design through convex optimization. © 1998 John Wiley & Sons, Ltd. 相似文献
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The problem of finding stabilizing controllers for switched systems is an area of much research interest as conventional concepts from continuous time and discrete event dynamics do not hold true for these systems.Many solutions have been proposed,most of which are based on finding the existence of a common Lyapunov function(CLF) or a multiple Lyapunov function(MLF) where the key is to formulate the problem into a set of linear matrix inequalities(LMIs).An alternative method for finding the existence of a CLF by solving two sets of linear inequalities(LIs) has previously been presented.This method is seen to be less computationally taxing compared to methods based on solving LMIs.To substantiate this,the computational ability of three numerical computational solvers,LMI solver,cvx,and Yalmip,as well as the symbolic computational program Maple were tested.A specific switched system comprising four second-order subsystems was used as a test case.From the obtained solutions,the validity of the controllers and the corresponding CLF was verified.It was found that all tested solvers were able to correctly solve the LIs.The issue of rounding-off error in numerical computation based software is discussed in detail.The test revealed that the guarantee of stability became uncertain when the rounding off was at a different decimal precision.The use of different external solvers led to the same conclusion in terms of the stability of switched systems.As a result,a shift from using a conventional numerical computation based program to using computer algebra is suggested. 相似文献
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This note investigates the robust stability of uncertain linear time-invariant systems in polytopic domains by means of parameter-dependent linear matrix inequality (PD-LMI) conditions, exploiting some algebraic properties provided by the uncertainty representation. A systematic procedure to construct a family of finite-dimensional LMI relaxations is provided. The robust stability is assessed by means of the existence of a Lyapunov function, more specifically, a homogeneous polynomially parameter-dependent Lyapunov (HPPDL) function of arbitrary degree. For a given degree , if an HPPDL solution exists, a sequence of relaxations based on real algebraic properties provides sufficient LMI conditions of increasing precision and constant number of decision variables for the existence of an HPPDL function which tend to the necessity. Alternatively, if an HPPDL solution of degree exists, a sequence of relaxations which increases the number of variables and the number of LMIs will provide an HPPDL solution of larger degree. The method proposed can be applied to determine homogeneous parameter-dependent matrix solutions to a wide variety of PD-LMIs by transforming the infinite-dimensional LMI problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite-dimensional LMI conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter-dependent solution of arbitrary degree. Illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature. 相似文献