共查询到20条相似文献,搜索用时 15 毫秒
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证明了一致指数稳定的非线性离散动力系统Lyapunov函数的存在性.由此证明非线性离散动力系统一致指数稳定等价于其线性化系统的一致指数稳定. 相似文献
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Andrea Bacciotti Alessandra Biglio 《NoDEA : Nonlinear Differential Equations and Applications》2001,8(4):425-438
We study stability and stabilizability properties of nonlinear discrete-time control systems by means of Liapunov functions.
We give a characterization of the uniform bounded-input-bounded-state stability property of nonlinear systems in the framework
of second Liapunov method. We find an explicit feedback law stabilizing a discrete-time control system affine-in-control under
the Jurdjevic-Quinn approach.
Received April 2000 相似文献
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Alexander J. Zaslavski 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):952-970
In this work we study the structure of approximate solutions of an autonomous discrete-time control system with a compact metric space of states X which is a subset of a finite-dimensional Euclidean space. This control system is described by a nonempty closed set Ω⊂X×X which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous function v:Ω→R1 which determines an optimality criterion. We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. Usually, in economic dynamics, the turnpike properties have been studied for systems such that all their good programs converge to a turnpike which was an interior point of Ω. In this paper we establish turnpike results for a large class of control systems for which the turnpike is not necessarily an interior point of Ω. 相似文献
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We consider parameter-dependent linear time-invariant discrete-time single input systems, where the system matrix and the input vector are assumed to depend continuously on a parameter varying over a compact interval. We face the problem of steering the zero state simultaneously arbitrarily close towards a given continuous family of desired terminal states with a finite parameter independent open-loop input sequence. Starting from existing sufficient conditions, which include simplicity of the eigenvalues of the system matrices, we examine the case of multiple eigenvalues. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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F. Tardella 《Journal of Optimization Theory and Applications》1989,60(1):105-116
We study some topological properties of the vector sum of two sets, and we introduce the concept of strong cone compactness, a slightly strengthened version of the notion of cone compactness, which is used frequently in vector optimization. Furthermore, we establish a generalization of the well-known fact that the continuous image of a compact set is compact. 相似文献
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Xuegong Tan 《Discrete Mathematics》2008,308(20):4786-4790
The k-dimensional folded Petersen graph, FPk, is an iterative Cartesian product on the simple Petersen graph. As an essential component of folded Petersen cube, folded Petersen graph has many important properties. In this paper, we prove that the 3k-wide diameter and 3k-fault diameter of k-dimensional folded Petersen graph is either 2k+1 or 2k+2. Furthermore, we show that FPk is interval monotone. 相似文献
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A map φ:X→X induces a linear operator T:C(X)→C(X) by composition: Tf(x)=f°φ(x). T and φ are termed weakly almost periodic if the sequence {Tn} is precompact in the weak operator topology. Using general structure theorems for weakly almost periodic operators, the properties of these point maps are studied from the viewpoint of dynamical systems. The structure of individual minimal sets and of the union M of all minimal sets of φ are investigated. One key result is that, if X is compact, then φ is a strongly almost periodic (i.e., has uniformly equicontinuous iterates) homeomorphisms of M and M is a retract of X. These and other general results are applied to the case where X is a manifold. Several results in which weak implies strong almost periodicity are obtained. 相似文献
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Panpan Gu 《Journal of Difference Equations and Applications》2018,24(9):1414-1428
This paper deals with the problem of iterative learning control for a class of discrete-time switched singular systems with arbitrary switching rules. According to the characteristics of the systems, two types of iterative learning algorithms are proposed and the corresponding convergence conditions of the algorithms are established. Under some given assumptions, the algorithms can ensure the system state converges to the desired state trajectory on a finite time interval. Finally, two numerical examples are constructed to support the theoretical analysis. 相似文献
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《Optimization》2012,61(4):343-354
In this paper we treat discrete-time stochastic control systems. Using corresponding results for systems, which are linear with respect to the state variables, we derive under convexity assumptions optimality conditions in form of maximum principles 相似文献
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In this paper, the properties of reachability, controllability and essential reachability of positive discrete-time linear control systems are studied. These properties are characterized in terms of the directed graph of the state matrix. From these characterizations canonical forms of those properties are deduced. 相似文献
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《Chaos, solitons, and fractals》2005,23(2):459-467
This paper discusses adaptive control of a class of discrete-time chaotic systems from a fuzzy control approach. Using the T–S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. The resulting adaptively controlled chaotic system is shown to be globally stable, and its robustness is discussed. A simulation example of the chaotic Henon map control is finally presented, to illustrate an application and the performance of the proposed control algorithm. 相似文献
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Doklady Mathematics - 相似文献
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Lin Zhu Yanjun Shen Cuicui Li 《Communications in Nonlinear Science & Numerical Simulation》2009,14(2):361-370
This paper deals with some finite-time control problems for uncertain discrete-time linear systems subject to exogenous disturbance. Sufficient conditions are presented for finite-time stabilization via state feedback. These conditions can be reduced to feasibility problems involving linear matrix inequality (LMI). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, an example illustrates the proposed methodology. 相似文献