Exponential stabilization of networked control systems and design of switching controller

This paper deals with the problem of switching between an open-loop estimator and a close-loop estimator for compensating transmission error and packet dropout of networked control systems. Switching impulse is considered in order to reduce the error between theory and application, a sufficient condition for exponential stabilization of networked control systems under a given switching rule is presented by multiple Lyapunov-like functions. These results are presented for both continuous-time and discrete-time domains. Controllers are designed by means of linear matrix inequalities. Sim- ulation results show the feasibility and efficiency of the proposed method.

BOUNDEDNESS AND EXPONENTIAL STABILIZATION IN A PARABOLIC-ELLIPTIC KELLER–SEGEL MODEL WITH SIGNAL-DEPENDENT MOTILITIES FOR LOCAL SENSING CHEMOTAXIS

In this paper we consider the initial Neumann boundary value problem for a degenerate Keller-Segel model which features a signal-dependent non-increasing motility function.The main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes unbounded.In the current work,we are interested in the boundedness and exponential stability of the classical solution in higher dimensions.With the aid of a Lyapunov functional and a delicate Alikakos-Moser type iteration,we are able to establish a time-independent upper bound of the concentration provided that the motility function decreases algebraically.Then we further prove the uniform-in-time boundedness of the solution by constructing an estimation involving a weighted energy.Finally,thanks to the Lyapunov functional again,we prove the exponential stabilization toward the spatially homogeneous steady states.Our boundedness result improves those in[1]and the exponential stabilization is obtained for the first time.

Delay-dependent robust exponential stabilization for uncertain systems with interval time-varying delays

New robust exponential stabilization criteria for interval time-varying delay systems with norm-bounded uncertainties are proposed. Based on the free-weighting matrices and new Lyapunov-Krasovskii functionals, such criteria are obtained by dealing with system model directly and designing memoryless state feedback controllers and expressed in terms of linear matrix inequalities （LMIs）. Moreover, the criteria are applicable to the case whether the derivative of the time-varying delay is bounded or not. The state decay rate is estimated by the corresponding LMIs. Numerical examples are given to illustrate the effectiveness of the proposed method.

Exponential Stabilization for C_0-Semigroups Under Compact Perturbation

It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.

Boundary Exponential Stabilization of a One-Dimensional Anti-Stable Wave Equation with Control Matched Disturbance

In this paper, we are concerned with output feedback stabilization for a one-dimensional anti-stable wave equation with disturbance. First, we design a disturbance estimator for the original system. Then, we propose an output feedback controller for the original system. By calculation, the closed-loop of original system is proved to be exponentially stable and well-posed. Finally, this paper is summarized.

EXPONENTIAL STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM WITH LOCALLY DISTRIBUTED FEEDBACKS

The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multiplier technique are applied.

Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space.The vehicle’s model is established on the matrix Lie group SE(3),which describes the configuration of rigid bodies globally and uniquely.We focus on the kinematic model of the underactuated vehicle,which features an underactuation form that has no sway and heave velocity.To compensate for the lack of these two velocities,we construct additional rotation matrices to generate a motion of rotation coupled with translation.Then,the state feedback is designed with the help of the logarithmic map,and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction.Later,the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance.Finally,simulation examples are provided to verify the effectiveness of the stabilization controller.

Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems

This paper proposes new sufficient conditions for the exponential stability and stabilization.of linear uncertain polytopic time-delay systems. The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities （LMIs） and we develop control design methods based on LMIs for solving stabilization problem. Our method consists of a combination of the LMI approach and the use of parameter-dependent Lyapunov functionals, which allows to compute simultaneously the two bounds that characterize the exponetial stability rate of the solution. Numerical examples illustrating the conditions are given.

pth-Moment Stabilization of Hybrid Stochastic Differential Equations by Discrete-Time Feedback Control

The given unstable hybrid stochastic differential equation is stabilized in the sense of p th-moment exponential stability.We achieve the results by feedback controls based on the discrete-time state and mode observations.The upper bound on the duration between two consecutive observations is obtained as well.Finally,a numerical example is given to verify the validity of the theoretical conclusions.

STABILIZATION OF VIBRATING BEAM BY VELOCITY FEEDBACK CONTROL

A flexible structure consisting of a Euler-Bernoulli beam with co-located sensors and actuators is considered. The control is a shear force in proportion to velocity. It is known that uniform exponential stability can be achieved with velocity feedback. A sensitivity asymptotic analysis of the system's eigenvalues and eigenfunctions is set up. The authors prove that, for K-1 epsilon (0, + infinity), all of the generalized eigenvectors of A form a Riesz basis of H. It is also proved that the optimal exponential decay rate can be obtained from the spectrum of the system for 0 < K-1 < + infinity.

Equivalence between the internal observability and equation

This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.

Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global exponential stability in the case of discrete-time positive homogeneous systems with an order less than one with time-varying delays.

Global exponential stability of Cohen-Grossberg neural networks with variable delays

A class of generalized Cohen-Grossberg neural networks（CGNNs） with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.

ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.

Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays

In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks （RNNs） with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.

Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

New Robust Exponential Stability Analysis for Uncertain Neural Networks with Time-varying Delay

In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional,some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs).Numerical examples are presented to show the effectiveness of the proposed method.

A new result on global exponential robust stability of neural networks with time-varying delays

In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.

GLOBAL ATTRACTIVITY AND GLOBAL EXPONENTIAL STABILITY FOR DELAYED HOPFIELD NEURAL NETWORK MODELS

Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.

GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SOLUTIONS TO THE QUASILINEAR THERMO-DIFFUSION EQUATIONS WITH SECOND SOUND

This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.