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1.
V. A. Zaitsev 《Differential Equations》2013,49(12):1619-1628
We obtain new sufficient conditions for the uniform global asymptotic stabilization of the zero solution of an affine control system with periodic coefficients and some corollaries for bilinear control systems. 相似文献
2.
V. A. Zaitsev 《Differential Equations》2013,49(1):101-111
The Jurdjevic-Quinn theorem on the global asymptotic stabilization of the origin is generalized to nonlinear time-varying affine control systems with periodic coefficients. The proof is based on the Krasovskii theorem on the global asymptotic stability for periodic systems and the introduced notion of “commutator” for two vector fields one of which is time-varying. The obtained sufficient conditions for stabilization are applied to bilinear control systems with periodic coefficients. We construct a control periodic in t in the form of a quadratic form in x that asymptotically stabilizes the zero solution of a bilinear periodic system with a time-invariant drift. 相似文献
3.
4.
G. Leitmann 《Journal of Optimization Theory and Applications》1979,27(1):99-106
We consider a class of linear dynamical systems with bounded, Lebesgue-measurable uncertainties in the system and input matrices as well as in the input itself. A state feedback control is derived, which guarantees global, uniform asymptotic stability of the zero state; this control is continuous, except at the zero state.This paper is based in part on research supported by the National Science Foundation. 相似文献
5.
Muhammad Rehan Keum-Shik Hong Shuzhi Sam Ge 《Nonlinear Analysis: Real World Applications》2011,12(3):1786-1796
This paper discusses stabilization and tracking control using linear matrix inequalities for a class of systems with Lipschitz nonlinearities. A nonlinear state feedback stabilization control is proposed for systems containing a more general case of Lipschitz nonlinearity. The main objective of the present study is to provide, for multi-input multi-output nonlinear systems, a tracking control approach based on nonlinear state feedback, which guarantees global asymptotic output and state tracking with zero tracking error in the steady state. Further, the tracking control is formulated for optimal disturbance rejection, using gain reduction based performance criteria. The proposed methodologies are illustrated herein using two simulation examples of chaotic and unstable dynamical systems. 相似文献
6.
We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by state feedback.
We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a right
factorization over H-infinity. A necessary and sufficient condition in terms of an (arbitrary) realization is that each state
which can be reached in a finite time from the zero initial state has a finite cost. Another equivalent condition is that
the control Riccati equation has a solution (in general unbounded and even non densely defined). The optimal state feedback
input-output stabilization problem can then be solved explicitly in terms of the smallest solution of this control Riccati
equation. We further show that after renorming the state space in terms of the solution of the control Riccati equation, the
closed-loop system is not only input-output stable, but also strongly internally stable.
Received: July 4, 2007. Revised: October 17, 2007. 相似文献
7.
We study the stability of the zero solution to a nonlinear system of ordinary differential equations on the base of its Takagi–Sugeno (TS) representation. As is known, the most constructive stability and stabilization conditions for TS systems stated as linear matrix inequalities are established with the help of a general quadratic Lyapunov function (GQLF). However, such conditions are often too rigid. Using a modification of the Lyapunov direct method, we propose asymptotic stability conditions with weaker requirements to GQLF. They allow an application to a wider class of systems. We also give some illustrative examples. 相似文献
8.
Yoshiaki Muroya 《Journal of Mathematical Analysis and Applications》2007,326(1):372-389
In this paper, we consider separable nonlinear delay differential systems and we establish conditions for global asymptotic stability of the zero solution. Applying these, we offer improved 3/2-type criteria for global asymptotic stability of nonautonomous Lotka-Volterra systems with delays. 相似文献
9.
Stability and stabilization of a class of nonlinear impulsive hybrid systems based on FSM with MDADT
The issue of stability and stabilization for a class of nonlinear impulsive hybrid systems based on finite state machine (FSM) with mode-dependent average dwell time (MDADT) is investigated in this paper. The concepts of global asymptotic stability and global exponential stability are extended for the systems, and the multiple Lyapunov functions (MLFs) are constructed to prove the sufficient conditions of global asymptotic stability and global exponential stability, respectively. Furthermore, the method of stabilization is also given for the hybrid systems. The application of MLFs and MDADT leads to a reduction of conservativeness in contrast with classical Lyapunov function. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed approach. 相似文献
10.
We extend the well-known Artstein-Sontag theorem by introducing the concept of control Lyapunov function for the notion of
nonuniform in time global asymptotic stability in probability of stochastic differential system, when both the drift and diffusion
terms are affine in the control. The main results of our work enable us to derive the necessary and sufficient conditions
for feedback stabilization for affine in the control systems. 相似文献
11.
We propose an approach to output stabilization of multiply connected control systems with uncertainty based on structural
decomposition of the original system and asymptotic invariance methods. The proposed approach solves the stabilization problem
for minimum-phase systems. Bounds are obtained on the rate of convergence of the stabilization algorithms. Conditions are
derived expanding the class of vector controlled systems with uncertainty that are stabilizable by asymptotic invariance methods. 相似文献
12.
This paper investigates the problem of global fixed-time stabilization for a class of uncertain switched nonlinear systems with the general powers, namely, the powers of the considered systems can be different odd rational numbers, even rational numbers or both odd and even rational numbers. By skillfully using the common Lyapunov function method and the adding a power integrator technique, a common state feedback control strategy is developed. It is proved that the proposed controller can guarantee that the state of the resulting closed-loop system converges to zero for any given fixed time under arbitrary switchings. Simulation results of the liquid-level system are provided to show the effectiveness of the proposed method. 相似文献
13.
《随机分析与应用》2013,31(6):1255-1282
Abstract The purpose of this paper is to give a systematic method for global asymptotic stabilization in probability of nonlinear control stochastic differential systems the unforced dynamics of which are Lyapunov stable in probability. The approach developed in this paper is based on the concept of passivity for nonaffine stochastic differential systems together with the theory of Lyapunov stability in probability for stochastic differential equations. In particular, we prove that, as in the case of affine in the control stochastic differential systems, a nonlinear stochastic differential system is asymptotically stabilizable in probability provided its unforced dynamics are Lyapunov stable in probability and some rank conditions involving the affine part of the system coefficients are satisfied. Furthermore, for such systems, we show how a stabilizing smooth state feedback law can be designed explicitly. As an application of our analysis, we construct a dynamic state feedback compensator for a class of nonaffine stochastic differential systems. 相似文献
14.
关于系统的状态反馈稳定性问题的研究一直是现代控制理论研究的重要问题之一.广义分布参数系统是比分布参数系统更广的一类系统,在研究复合材料热导体中的温度分布等问题时会出现这样的系统.本文讨论了H ilbert空间中一阶广义分布参数系统的状态反馈稳定性问题.应用泛函分析及线性算子半群理论的方法给出了使闭环广义分布参数系统渐进稳定的充要条件,充分条件及状态反馈的构造性表达式.这对研究广义分布参数系统的状态反馈稳定性问题具有重要的理论价值. 相似文献
15.
Olivier Glass 《Journal of Differential Equations》2008,245(6):1584-1615
We investigate the problems of exact controllability and asymptotic stabilization of the Camassa-Holm equation on the circle, by means of a distributed control. The results are global, and in particular the control prevents the solution from blowing up. 相似文献
16.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(12):4100-4113
In this paper, we consider the problem of synchronizing a master–slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master–slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master–slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master–slave chaotic system based on Chua’s circuit. 相似文献
17.
ONGLOBALASYMPTOTICSTABILITYOFTHEZEROSOLUTIONOFAGENERALIZEDLIENARD′SSYSTEMPENGLEQUNANDHUANGLIHONGAbstract:Inthispaper,westudyt... 相似文献
18.
Y. Yu 《Journal of Optimization Theory and Applications》1983,41(3):503-508
This note concerns the stabilization problem for linear delay systems containing uncertain elements. If the so-called matching conditions are satisfied and the uncertainties in the control matrix are not too large, there exist linear current-response feedback controls which guarantee asymptotic stability of the zero response of the system, no matter what the uncertainties and initial conditions are. 相似文献
19.
V. A. Zaitsev 《Differential Equations》2013,49(3):336-345
We prove sufficient conditions for the uniform global asymptotic stabilization of the origin for bilinear time-varying systems that can be reduced by a Lyapunov transformation to bilinear periodic systems with time-invariant drift, in particular, for bilinear periodic systems with time-varying drift. We obtain corollaries for consistent systems. 相似文献
20.
Alexander Zlotnik 《Mathematical Methods in the Applied Sciences》2003,26(8):671-690
We consider an initial–boundary value problem for a system of quasilinear equations for one‐dimensional flows of a viscous compressible barotropic fluid with large data. An outer pressure (possibly zero) is prescribed on one of the boundaries; also a self‐gravitation is taken into account. The case of the stationary pressure with possible degeneration is studied. For a general non‐monotone state function, either global estimates for the solution and its stabilization are proved or the growth of the fluid volume is bounded from below as t → ∞. For the power state function, in addition, stabilization rate estimates (of the power type) are given. The study is accomplished in the Lagrangian mass co‐ordinates. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献