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Exponential Stability and Stabilization for Quadratic Discrete‐Time Systems with Time Delay 下载免费PDF全文
In this note, we deal with the exponential stability and stabilization problems for quadratic discrete‐time systems with time delay. By using the quadratic Lyapunov function and a so called ‘Finsler's lemma', delay‐independent sufficient conditions for local stability and stabilization for quadratic discrete‐time systems with time delay are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper. 相似文献
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Robust stability and stabilization of discrete singular systems: an equivalent characterization 总被引:3,自引:0,他引:3
This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach. 相似文献
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广义不确定系统鲁棒稳定性及鲁棒镇定的矩阵不等式方法 总被引:6,自引:1,他引:5
考虑广义不确定系统的鲁棒稳定性及鲁棒镇定问题.提出了广义不确定系统'广义二
次稳定'及'广义二次可镇定'的概念,利用矩阵不等式,分别得到了所考虑广义不确定系统广义
二次稳定及广义二次可镇定的充要条件,而且,使广义不确定系统鲁棒镇定的状态反馈控制律
的设计可通过求解一给定的矩阵不等式而得到. 相似文献
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从全新的二次型供给率的耗散角度,研究了线性时滞系统的二次稳定性和耗散控制问题,给出了线性矩阵不等式(LMI)形式的充分条件。而且,考虑了时滞系统在状态反馈控制器和动态输出反馈控制器作用下的闭环系统的二次稳定和耗散性问题,同样给出了LMI形式的充分条件,并通过线性矩阵不等式的可行解构造出耗散状态反馈控制律和动态输出反馈控制律。 相似文献
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This paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete-time systems with state delay. The system under consideration involves state time delay and time-varying norm-bounded parameter uncertainties appearing in all the matrices of the state-space model. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities, respectively. A robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities. Two examples are presented to demonstrate the effectiveness of the proposed approach. 相似文献
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This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results. 相似文献
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J. P. Emelianova P. V. Pakshin K. Gałkowski E. Rogers 《Automation and Remote Control》2014,75(5):845-858
This paper considers systems with two-dimensional dynamics (2D systems) described by the continuous-time nonlinear state-space Roesser model. The sufficient conditions of exponential stability in terms of vector Lyapunov functions are established. These conditions are then applied to analysis of the absolute stability of a certain class of systems comprising a linear continuous-time plant in the form of the Roesser model with a nonlinear characteristic in the feedback loop, which satisfies quadratic constraints. The absolute stability conditions are reduced to computable expressions in the form of linear matrix inequalities. The obtained results are extended to the class of continuous-time systems governed by the Roesser model with Markovian switching. The problems of absolute stability and stabilization via state- and output-feedback are solved for linear systems of the above class. The solution procedures for these problems are in the form of algorithms based on linear matrix inequalities. 相似文献
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Shengyuan Xu Van Dooren P. Stefan R. Lam J. 《Automatic Control, IEEE Transactions on》2002,47(7):1122-1128
Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method 相似文献
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In this paper, finite‐time stability and stabilization problems for a class of linear stochastic systems are studied. First, a new concept of finite‐time stochastic stability is defined for linear stochastic systems. Then, based on matrix inequalities, some sufficient conditions under which the stochastic systems are finite‐time stochastically stable are given. Subsequently, the finite‐time stochastic stabilization is studied and some sufficient conditions for the existence of a state feedback controller and a dynamic output feedback controller are presented by using a matrix inequality approach. An algorithm is given for solving the matrix inequalities arising from finite‐time stochastic stability (stabilization). Finally, two examples are employed to illustrate the results. 相似文献
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Wei-Jie Mao Jian Chu 《Automatic Control, IEEE Transactions on》2003,48(6):1007-1012
This note presents necessary and sufficient conditions for the quadratic stability and stabilization of dynamic interval systems. The results are obtained in terms of linear matrix inequalities (LMIs) and extended to the quadratic stability and stabilization of linear systems with uncertain parameters. With the powerful LMI toolbox, it is very convenient to solve these problems. The illustrative examples show that this method is effective and less conservative to check the robust stability and to design the stabilizing controller for dynamic interval systems. 相似文献
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Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to the stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach. 相似文献
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关于不确定对称组合系统的稳定化 总被引:2,自引:0,他引:2
研究不确定对称组合系统的二次稳定化问题,给出这类系统可二次稳定的一些充分条件
及计算反馈控制律的方法.这些条件的检验和反馈控制律的计算都由两个低阶系统关于相应
问题的求解来完成. 相似文献
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This paper deals with the controller design problem of nonlinear quadratic Markov jumping systems with input saturation. Both mode-dependent and mode-independent state feedback controllers are designed. By using the concept of domain of attraction in mean square sense, sufficient conditions for stochastic stabilisation for nonlinear quadratic systems are derived in terms of linear matrix inequalities. Certain existing results are improved. Simulation examples are presented to illustrate the effectiveness of the proposed technique. 相似文献
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This paper considers the robust-optimal design problems of output feedback controllers for linear systems with both time-varying elemental (structured) and norm-bounded (unstructured) parameter uncertainties. Two new sufficient conditions are proposed in terms of linear-matrix-inequalities (LMIs) for ensuring that the linear output feedback systems with both time-varying elemental and norm-bounded parameter uncertainties are asymptotically stable, where the mixed quadratically-coupled parameter uncertainties are directly considered in the problem formulation. A numerical example is given to show that the presented sufficient conditions are less conservative than existing ones reported recently. Then, by integrating the hybrid Taguchi-genetic algorithm (HTGA) and the proposed LMI-based sufficient conditions, a new integrative approach is presented to find the output feedback controllers of the linear systems with both time-varying elemental and norm-bounded parameter uncertainties such that the control objective of minimizing a quadratic integral performance criterion subject to the stability robustness constraint is achieved. A design example of the robust-optimal output feedback controller for the AFTI/F-16 aircraft control system with the time-varying elemental parameter uncertainties is given to demonstrate the applicability of the proposed new integrative approach. 相似文献