Stability Analysis for Sampled-Data Systems with Input Delay

On the stability of certain systems under resonance conditions

Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the asymptotic stability of such cycles. In particular, we found a sufficient condition for asymptotic stability, and we gave algebraic criteria for deciding when this condition is also necessary. These criteria are satisfied for cycles in R3.Field and Swift, and Hofbauer, considered examples in R4 for which our sufficient condition for stability is not optimal. They obtained necessary and sufficient conditions for asymptotic stability using a transition-matrix technique.In this paper, we combine our previous methods with the transition-matrix technique and obtain necessary and sufficient conditions for asymptotic stability for a larger class of heteroclinic cycles. In particular, we obtain a complete theory for ‘simple’ heteroclinic cycles in R4 (thereby proving and extending results for homoclinic cycles that were stated without proof by Chossat, Krupa, Melbourne and Scheel). A partial classification of simple heteroclinic cycles in R4 is also given. Finally, our stability results generalize naturally to higher dimensions and many of the higher-dimensional examples in the literature are covered by this theory.

Stability analysis of sampled-data systems considering time delays and its application to electric power markets

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

The stability problem of a dynamic quantized UAV airborne system with time-varying delay and packet losses is studied in this paper. Sufficient condition for asymptotic stability of the system is considered in terms of matrix inequalities. Finally an illustrative example demonstrates the effectiveness of the proposed method.

The positivity and asymptotic stability of the discrete-time nonlinear systems are addressed. Necessary and sufficient conditions for the positivity of the systems and sufficient conditions for asymptotic stability of the positive systems are established. The proposed stability tests are based on Lyapunov method. The effectiveness of the tests are demonstrated on examples.

An enhanced looped-functional framework for stability analysis of sampled-data systems

A secondary controller which uses a number of Annular Momentum Control Devices (AMCD's) for enhancement of structural damping in large flexible space structures is investigated. The closed-loop secondary controller is shown to be equivalent to a certain closed-loop optimal linear regulator, and the necessary and sufficient conditions for asymptotic stability are obtained. Sufficient conditions for asymptotic stability are also obtained which are much less restrictive than those obtained in an earlier paper. Design of a robust stable primary controller is also discussed.

In this article, using the method of stochastic Lyapunov functions (SLF), we obtain new algebraic criteria and sufficient conditions for the asymptotic stability with probability 1 for the solutions of a system of linear stationary difference equations with random (of the type of a vector "white" sequence of random variables) coefficients, which are discrete analogs of the conditions established earlier by several authors for stochastic Ito equations with continuous time. We assume that in the absence of parametric random perturbations, an unperturbed determined system of difference equations is asymptotically Lyapunov stable (the matrix A of the system is convergent). The conditions are formulated either in terms of the negative definiteness of certain matrix relations, involving the matrix A and the matrices of the parametric perturbations Bi, i = i, 2 .... , r (sufficient conditions, which in many cases are nearly necessary), or in terms of the existence of a positive-definite solution H of the Sylvester matrix algebraic equation e

Chapter 4 - On Unknown Input Observer Design for Linear Systems With Delays in States and Inputs

Many ocean missions require one or more AUVs. However, due to the time-variant communication delay, the implementation of tracking task is more challenging. In this chapter, the problems of single single-vehicle tracking and multivehicle tracking are studied. With consideration of time-variant communication delay, two model-free PD tracking controllers are developed. Lyapunov–Krasovskii functions are employed to establish sufficient conditions for asymptotic stability. In particular, the relationship between controller gains and time delay is presented by using LMI, such that the allowable upper bound of time delay can be calculated. Finally, the effectiveness of the proposed approach is verified by simulation and experiment.

Many marine missions demand a single remotely operated underwater vehicle (ROV) or multiple ROVs to achieve position tracking. However, the time-varying communication delay in water makes it challenging to achieve the tracking task. This paper is concerned with single-vehicle tracking and multi-vehicle tracking problems. With the consideration of time-varying communication delay, two model-free proportional-derivative (PD) tracking controllers are designed. For the proposed controllers, Lyapunov–Krasovskii functions are constructed to analyze the stability, and then sufficient conditions for asymptotic stability are presented. In particular, the relationship between controller gains and time delay is established by using linear matrix inequality (LMI), such that the allowable upper bound of time delay can be calculated. Finally, simulation and experiment results are performed to validate the effectiveness.

H[formula omitted] synchronization of semi-Markovian jump neural networks with random sensor nonlinearities via adaptive event-triggered output feedback control

For switched fuzzy systems with time-varying delays, this paper designs the observers to estimate unmeasured state variables in the system when the state of the system is unmeasurable, and designs the memory state feedback controller which introduce the past information of the system state to eliminate the influence of time delay on the system. Based on the definition of Lyapunov stability, a sufficient condition of asymptotic stability of the closed-loop system under a given switching law is obtained, then convert it into a linear matrix inequality form that MATLAB can solve, and obtain the condition that meet the observer gain and the controller gain. Finally, the state curve and control curve of memory state feedback control are given by simulink, which verifies the effectiveness and feasibility of the proposed method.

This paper is concerned with stability analysis and output feedback control design of fuzzy bilinear systems with time-varying delay. First, we consider the stability of the closed-loop systems by assuming a special form of a fuzzy controller. A delay-dependent stability condition, which is less conservative than delay-independent one, is given in terms of linear matrix inequality (LMI). Based on such a stability condition, we propose a state feedback stabilizing control design for fuzzy bilinear systems with time-varying delays. Next, we consider a fuzzy observer design for the same class of systems, and propose an observer design based on another delay-dependent condition. Then, we show that state feedback stabilizing controller and observer make an output feedback stabilizing controller. Finally, we give a numerical example to illustrate our design procedures and to show the effectiveness of our approach.