共查询到20条相似文献,搜索用时 250 毫秒
1.
This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. System robustness is also studied when the norm-bounded uncertainties are considered. LMI delay-dependent sufficient conditions for stability, stabilizability, and system robustness are established to check whether a system of this class is stable and/or stabilizable. Numerical examples are provided to show the usefulness of the proposed results. 相似文献
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The problem of the stabilizability of stochastic nonlinear hybrid systems with a Markovian or any switching rule is considered. Using the Lyapunov technique sufficient conditions for the asymptotic stabilizability in probability by a smooth controller in every structure are found. In particular, the asymptotic stabilizability in probability problem of stochastic bilinear hybrid systems with a Markovian or any switching rule is discussed and a closed-loop controller is found. Also the sufficient conditions for the exponential mean-square stabilizability for bilinear hybrid systems with any switching based on the Lie algebra approach are formulated and an open-loop controller is designed. The obtained results are illustrated by examples and simulations. 相似文献
4.
《Optimization》2012,61(6):912-924
In this paper, we consider the questions of stabilization of perturbed (or uncertain) linear systems in Hilbert space. Perturbations of the system operator represent the uncertainty in the modelling process and could be bounded or even unbounded. Sufficient conditions are presented that guarantee stabilizability of the perturbed system given that the nominal (unperturbed) system is stabilizable. In particular it is shown that for certain class of perturbations weak and strong stabilizability properties are preserved for the same state feedback control. Two numerical examples are given to illustrate our theory. 相似文献
5.
A two-component reaction–diffusion system modelling a class of spatially structured epidemic systems is considered. The system describes the spatial spread of infectious diseases mediated by environmental pollution. The internal zero stabilization is investigated. We provide necessary conditions of stabilizability and sufficient conditions of stabilizability. In the affirmative case a simple feedback stabilizing control is indicated. It shows that it is possible to diminish exponentially the epidemic process, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain (think globally, act locally). 相似文献
6.
M. Najafi 《Mathematical and Computer Modelling》2009,49(1-2):46-54
In this paper, the stabilizability conditions of a system of wave equations, coupled in parallel with distributed springs and viscous dampers, are investigated via energy perturbation and decomposition methods for different wave propagation speeds. 相似文献
7.
A short survey on delayed feedback stabilization is given. The Huijberts–Michiels–Nijmeijer problem on the delayed feedback stabilization of unstable equilibria of two- and three-dimensional dynamical systems is considered. It is shown that the methods of delayed feedback stabilization of unstable periodic orbits can be used with advantage for the stabilization of unstable equilibria. An analytical study based on the D-decomposition method is given. Efficient necessary and/or sufficient conditions for the stabilizability of the systems in question are obtained in the form of explicit analytic expressions. These conditions define the boundaries of stabilizability domains in terms of system parameters. It follows from these conditions that the introduction of a delayed feedback control generally extends the possibilities of stationary stabilization of linear systems with delay-free feedback. 相似文献
8.
主要讨论基于开关控制的线性奇异系统的二次状态反馈镇定问题.利用二次反馈镇定的概念,给出了线性奇异系统基于异步开关控制的二次状态反馈镇定问题可解的两个充分条件.进一步,对于带有范数有界的不确定项的奇异线性系统,给出了其可以基于异步开关控制的二次状态反馈鲁棒镇定的可解性条件. 相似文献
9.
J. Zabczyk 《Applied Mathematics and Optimization》1989,19(1):1-9
This paper discusses the robustness of exponentially stabilizable systems and the relationships between controllability and stabilizability. An absolute bound on the robustness index of a controlled system is obtained and an extension of Brockett's necessary conditions for stabilizability is also given.This research was supported by S.E.R.C. Contract No. GR/B/9116.7. The paper was completed in Spring 1985, when the author was with the Department of Mathematics, Heriot-Watt University, Edinburgh, Scotland. 相似文献
10.
《Nonlinear Analysis: Hybrid Systems》2008,2(3):750-764
A complete characterization of stabilizability for linear switching systems is not available in the literature. In this paper, we show that the asymptotic stabilizability of linear switching systems is equivalent to the existence of a hybrid Lyapunov function for the controlled system, for a suitable control strategy. Further, we prove that asymptotic stabilizability of a switching system with minimum dwell time, is equivalent to Input to State Stability (ISS) of the controlled switching system, with a stabilizing control law. We then derive some structural reductions of the hybrid state space, which allow a decomposition of the original problem into simpler subproblems. The relationships between this approach and the well-known Kalman decomposition of linear dynamic control systems are explored. 相似文献
11.
William L. Green 《Numerical Functional Analysis & Optimization》2013,34(3):235-252
This paper considers stabilizability by closed loop feedback for single-input systems defined over a commutative normed algebra B0. Sufficient conditions for such stabilizability are given. These conditions are weaker than invertibility of the reachability matrix over B0 or over its completion. These results are applied to examples from two- dimensional digital filtering to establish the existence of a feedback whose Fourier transform is a polynomial in z and z. 相似文献
12.
Rigoberto Medina 《Journal of Difference Equations and Applications》2013,19(5):697-708
In this paper, we give sufficient conditions for the exponential stabilizability of a class of perturbed non-autonomous difference equations with slowly varying coefficients. Under appropriate growth conditions on the perturbations, we establish explicit results concerning the feedback exponential stabilizability. 相似文献
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M. M. Shumafov 《Russian Mathematics (Iz VUZ)》2010,54(12):76-78
We consider a static stabilization problem for a two-dimensional linear time-invariant control system with a delayed feedback.
We obtain the necessary and sufficient conditions for the stabilizability of the system under consideration. The theorems
proved in this paper show that such a delayed feedback approach is efficient in stabilizing the second-order linear systems. 相似文献
14.
《Nonlinear Analysis: Hybrid Systems》2008,2(1):196-208
In this paper, we report some new results on practical asymptotic stabilizability of switched systems consisting of affine subsystems. We first briefly review some practical asymptotic stabilizability notions and some results from our previous papers. Then we propose a new approach to estimate the region of attraction for switched affine systems. Based on this new approach, we present several new sufficient conditions for the practical asymptotic stabilizability and global practical asymptotic stabilizability of such systems. Finally, a computational approach to check the new sufficient conditions is proposed and it is applied to several numerical examples. 相似文献
15.
We propose a new quadratic control problem for linear periodic systems which can be finite or infinite dimensional. We consider both deterministic and stochastic cases. It is a generalization of average cost criterion, which is usually considered for time-invariant systems. We give sufficient conditions for the existence of periodic solutions.Under stabilizability and detectability conditions we show that the optimal control is given by a periodic feedback which involves the periodic solution of a Riccati equation. The optimal closed-loop system has a unique periodic solution which is globally exponentially asymptotically stable. In the stochastic case we also consider the quadratic problem under partial observation. Under two sets of stabilizability and detectability conditions we obtain the separation principle. The filter equation is not periodic, but we show that it can be effectively replaced by a periodic filter. The theory is illustrated by simple examples.This work was done while this author was a visiting professor at the Scuola Normale Superiore, Pisa. 相似文献
16.
I. R. Petersen 《Journal of Optimization Theory and Applications》1988,57(3):439-461
This paper is concerned with the problem of stabilizing an uncertain linear system using state feedback control. The uncertain
systems under consideration are described by state equations containing unknown but bounded uncertain parameters. The uncertain
parameters are classified into two types: either constant or time-varying. Indeed, the main feature of this paper is that
it allows one to exploit the fact that some of the uncertain parameters are constant. In order to investigate the question
of stabilizability, quadratic Lyapunov functions are used. Hence, the paper deals with the notion of quadratic stabilizability.
The main result of the paper is a necessary and sufficient condition for the quadratic stabilizability of the uncertain systems
under consideration. 相似文献
17.
In this paper, we consider the quadratic stabilizability via state feedback for a particular class of switched systems that evolve on a non-uniform time domain by introducing time scales theory. The system considered switches between a continuous-time subsystem with variable lengths and a discrete-time subsystem with variable discrete step sizes. Necessary and sufficient conditions are derived to guarantee the quadratic stability of this class of switched systems via a switching state feedback law based on the existence of a common positive definite matrix satisfying the quadratic stabilizability condition by considering that the two subsystems are unstable. By state feedback, we mean that the switching among subsystems depends on the system states. Current results for this kind of state switching feedback control are derived only for switched systems evolving on a continuous time domain or a discrete time domain with fixed step’s size. These results are not applicable for the particular class of switched systems where there is a mixing between the continuous and discrete dynamics. This motivates the derivation of a new and more general state feedback control law for switched systems in this work. A numerical example illustrating the results is presented. 相似文献
18.
Robust exponential stability and stabilizability of linear parameter dependent systems with delays 总被引:1,自引:0,他引:1
T. Botmart 《Applied mathematics and computation》2010,217(6):2551-2566
The robust exponential stability and stabilizability problems are addressed in this paper for a class of linear parameter dependent systems with interval time-varying and constant delays. In this paper, restrictions on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive delay-dependent exponential stability and stabilizability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to illustrate the effectiveness of our theoretical results. 相似文献
19.
This paper deals with the class of continuous-time linear systems with Markovian jumps and multiple time delays. The systems that we are treating are assumed to have time-varying delays in their dynamics which can be different and also have uncertainties in the system parameters. The time-varying structure of the bounded uncertainties is considered. Delay-dependent conditions for stochastic stability and stochastic stabilizability and their robustness are considered. A design algorithm for a stabilizing memoryless controller is proposed. All the results are given in the LMI formalism. 相似文献