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1.
This paper is concerned with the problem of finite-time L1 control for a class of positive switched linear systems with time-varying delay. Firstly, by using the average dwell time approach, sufficient conditions which can guarantee the L1 finite-time boundedness of the underlying system are given. Then, in virtue of the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with L1-gain performance. All the obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be solved conveniently. Finally, an example is given to illustrate the efficiency of the proposed method.  相似文献   

2.
This paper investigates the robust finite-time H control problem for a class of uncertain switched neutral systems with unknown time-varying disturbance. The uncertainties under consideration are norm bounded. By using the average dwell time approach, a sufficient condition for finite-time boundedness of switched neutral systems is derived. Then, finite-time H performance analysis for switched neutral systems is developed, and a robust finite-time H state feedback controller is proposed to guarantee that the closed-loop system is finite-time bounded with H disturbance attenuation level γ. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.  相似文献   

3.
This paper investigates the problem of robust L2L filtering for continuous-time switched systems under asynchronous switching. When there exists asynchronous switching between the filter and the system, based on the average dwell time approach, sufficient conditions for the existence of a linear filter that guarantee the filtering error system to be exponentially stable with a prescribed weighted L2L performance for switched systems are derived, and filter parameters can be obtained by solving a set of matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.  相似文献   

4.
In this paper, we study the stability problems and L2‐gain analysis for switched singular linear systems with jumps. Based on the concept of average impulsive interval, some novel sufficient conditions on the stability and L2‐gain for switched singular linear systems with jumps are developed. Two examples are given to illustrate the effectiveness of the results. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
This paper is concerned with the exponential stabilization and L2‐gain for a class of uncertain switched nonlinear systems with interval time‐varying delay. Based on Lyapunov–Krasovskii functional method, novel delay‐dependent sufficient conditions of exponential stabilization for a class of uncertain switched nonlinear delay systems are developed under an average dwell time scheme. Then, novel criteria to ensure the exponential stabilization with weighted L2‐gain performance for a class of uncertain switched nonlinear delay systems are established. Furthermore, an effective method is proposed for the designing of a stabilizing feedback controller with L2‐gain performance. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

6.
This paper is concerned with the finite-time quantized H control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.  相似文献   

7.
This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H finite-time boundedness for the class of singular stochastic systems. Designed algorithm for static output feedback controller is provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic H finite-time boundedness in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology.  相似文献   

8.
We consider affine control systems with the finite L2-gain property in the case the storage function is nondifferentiable. We generalize some classical results concerning the connection of the finite L2-gain property with the stability properties of the unforced system, the characterization of finite L2-gain by means of partial differential inequalities of the Hamilton-Jacobi type and the problem of giving to a system the finite L2-gain property by means of a feedback law. Moreover, we introduce and study the apparently new notion of exact storage function.  相似文献   

9.
This paper considers the L2 − L filtering problem for Markovian jump systems. The systems under consideration involve time-varying delays, disturbance signal and partly unknown transition probabilities. The aim of this paper is to design a filter, which is suitable for exactly known and partly unknown transition probabilities, such that the filtering error system is stochastically stable and a prescribed L2 − L disturbance attenuation level is guaranteed. By using the Lyapunov-Krasovskii functional, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of filter design for Markovian jump systems with partly unknown transition probabilities.  相似文献   

10.
11.
A linear homogeneous ODE is constructed, among whose solutions are all products of solutions of two given linear homogeneous ODE's Lm[u]=0, Mn[v]=0, in some classes. Its order is the minimum and its coefficients can be obtained by a finite number of rational operations and differentiations on the coefficients of Lm, Mn. The problem is considered (locally) both in the real and in the complex domain, around an isolated singularity. Examples are also given.  相似文献   

12.
This paper studies the robust and resilient finite-time H control problem for uncertain discrete-time nonlinear systems with Markovian jump parameters. With the help of linear matrix inequalities and stochastic analysis techniques, the criteria concerning stochastic finite-time boundedness and stochastic H finite-time boundedness are initially established for the nonlinear stochastic model. We then turn to stochastic finite-time controller analysis and design to guarantee that the stochastic model is stochastically H finite-time bounded by employing matrix decomposition method. Applying resilient control schemes, the resilient and robust finite-time controllers are further designed to ensure stochastic H finite-time boundedness of the derived stochastic nonlinear systems. Moreover, the results concerning stochastic finite-time stability and stochastic finite-time boundedness are addressed. All derived criteria are expressed in terms of linear matrix inequalities, which can be solved by utilizing the available convex optimal method. Finally, the validity of obtained methods is illustrated by numerical examples.  相似文献   

13.
We consider the elementary operator L, acting on the Hilbert-Schmidt Class C2(H), given by L(T)=ATB, with A and B bounded operators on H. We establish necessary and sufficient conditions on A and B for L to be a 2-isometry or a 3-isometry. We derive sufficient conditions for L to be an n-isometry. We also give several illustrative examples involving the weighted shift operator on l2 and the multiplication operator on the Dirichlet space.  相似文献   

14.
This paper considers the solution of weighted interpolation problems in model subspaces of the Hardy space H2 that are canonically isometric to Paley-Wiener spaces of analytic functions. A new necessary and sufficient condition is given on the set of interpolation points which guarantees that a solution in H2 can be transferred to a solution in a model space. The techniques used rely on the reproducing kernel thesis for Hankel operators, which is given here with an explicit constant. One of the applications of this work is to the finite-time controllability of diagonal systems specified by a C0 semigroup.  相似文献   

15.
The properties of L2-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are “two-wing” averages of martingale differences. The results constitute the first significant advancement in the theory of L2-approximable sequences since 1976 when Moussatat introduced a narrower notion of L2-generated sequences. The method relies on a study of certain linear operators in the spaces Lp and lp. A criterion of Lp-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.  相似文献   

16.
We consider linear operators T mapping a couple of weighted Lp spaces {Lp0(U0), Lp1(U1)} into {Lq0(V0),Lq1(V1)} for any 1?p0, p1, q0, q1?∞, and describe the interpolation orbit of any aLp0(U0)+Lp1(U1) that is we describe a space of all {Ta}, where T runs over all linear bounded mappings from {Lp0(U0),Lp1(U1)} into {Lq0(V0),Lq1(V1)}. We show that interpolation orbit is obtained by the Lions–Peetre method of means with functional parameter as well as by the K-method with a weighted Orlicz space as a parameter. To cite this article: V.I. Ovchinnikov, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 881–884.  相似文献   

17.
We study the complex Cauchy problem for a system of linear differential equations in the class of analytic functions with integral metric. In the case of a Hardy-Lebesgue type weighted L p -space, we obtain necessary and sufficient conditions for the local solvability of the problem.  相似文献   

18.
In this paper, we investigate the problems of robust delay-dependent ℒ2 gain analysis and feedback control synthesis for a class of nominally-linear switched discrete-time systems with time-varying delays, bounded nonlinearities and real convex bounded parametric uncertainties in all system matrices under arbitrary switching sequences. We develop new criteria for such class of switched systems based on the constructive use of an appropriate switched Lyapunov-Krasovskii functional coupled with Finsler’s Lemma and a free-weighting parameter matrix. We establish an LMI characterization of delay-dependent conditions under which the nonlinear switched delay system is robustly asymptotically stable with an ℒ2-gain smaller than a prescribed constant level. Switched feedback schemes, based on state measurements, output measurements or by using dynamic output feedback, are designed to guarantee that the corresponding switched closed-loop system enjoys the delay-dependent asymptotic stability with an ℒ2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples.  相似文献   

19.
In this article, we investigates finite-time H_∞ control problem of Markovian jumping neural networks of neutral type with distributed time varying delays. The mathematical model of the Markovian jumping neural networks with distributed delays is established in which a set of neural networks are used as individual subsystems. Finite time stability analysis for such neural networks is addressed based on the linear matrix inequality approach.Numerical examples are given to illustrate the usefulness of our proposed method. The results obtained are compared with the results in the literature to show the conservativeness.  相似文献   

20.
We obtain sufficient conditions for the boundedness and compactness of multidimensional integral operators with homogeneous kernels acting from a weighted L p -space to a weighted L q -space.  相似文献   

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