Essay Example on Stabilization of time delay systems has been an energetic research Field








In recent years the stability and stabilization of time delay systems has been an energetic research field 1 10 Since the latest literature demonstrate an increasing research interest in the study of linear systems subject to time delays Meanwhile time delay is a common phenomenon often encountered in dynamic models of many real world systems particularly the processes including transportation or propagation of material and data measurement and actuators delays cascaded electrical networks robotic systems information transmission delays neural networks 4 50 among other Therefore more importance needs to study the stability analysis of time delay systems Nowadays various efforts have been paid for linear systems with time delays and lots of related literature have been established on this issues based on the LMIs approach 14 46 Relevant books in the issue of time delay systems and uncertain systems are 6 7 among others Furthermore time delays may be varying and may occur in irregular approach or non differentiable 2 3 Also the existing stability conditions can be classified into two ways namely delay independent 22 and delay dependent 37 stability criteria In general delay dependent stabilization condition gives less conservative result than the delay independent one as it makes full use of information of the system 42 Thus the delay dependent stability criteria received increasing devotion compare than delay independent once 37 41 Corresponding author email jdcao seu edu cn 1On the other hand due to the presence of modeling errors variation of materials assets component nonlinearities and varying load environments in time delay systems the concerned system account carried the uncertainty component However parameter uncertainties are inevitable owing mainly to the modeling inaccuracies variations of the operating point and aging of the devices etc

Therefore the topic of robustness analysis has been taken into account in all types of time delay systems by several examiners In 19 a novel sorts of uncertainties have been proposed called as randomly occurring uncertainties ROUs due to the fact that the uncertainties may be subject to random changes in environmental situations for illustration repairs of components and sudden environmental disturbances and thus the uncertainties may occur in a probabilistic to obtain an exact mathematical model Hence it is an important to ensure that the model is stable with respect to the uncertainties and the robust stability analysis of time delay systems has received many research interest 20 29 In this regard many researchers have concentrated on stability and stabilization of time delay systems with randomly occurring uncertain parameters 30 33 34 Nowadays the studies of stabilization problem for various sorts of time delay systems have become an active research topics On the issue of stability analysis some effective controllers have been designed to stabilize the states of the dynamical systems such as sliding model 19 reliable control 33 non fragile control 29 H1 control 4 sampled data control 15 repetitive control 32 and so on

Nevertheless in recent years sampled data control is regarded as one of the major control techniques in the control community consistent attention has been devoted to the special class of time delay systems with sampled data control and has been fruitfully applied in lots of areas of science and engineering 10 17 For instance in 10 the authors have investigated the robust sampled data stabilization of linear systems by using Lyapunov technique and LMI approach Stability and stabilization of T S fuzzy systems via sampled data and state quantized controller is discussed in the work 15 In 13 the authors investigated sampled data H1 fuzzy filtering for nonlinear systems with missing measurements In 17 the authors have studied H2 and H1 control of time varying delay switched linear systems with application to sampled data control system Most recently in 44 the authors have deals with problem of robust extended dissipative control for sampled data Markov jump systems More precisely reliable state estimation of switched neutral system with nonlinear actuator faults via sampled data control is investigated in the work 31

An attractive quality about the problem considered in this paper is its possible application to control design of sampled data systems In fact it is well known that sampling can be represented in terms of delays 17 In particular non uniform sampling can be equally represented as a time varying delay performing on the input variables of the system 11 The recent literature on state feedback sampled data control design for linear time invariant systems developed in 12 are used to certificate the ones reported in this paper Nevertheless only few works have been established on the issue of stability analysis of time delay systems with randomly occurring uncertainties On the other side in order to achieve a less conservatism is main challenge on the issues of stability and stabilization of uncertain systems with time delays Thus our main goal in this literature is to achieve less conservative stability criterion Therefore there is still possible for a further investigates and development to the less conservatism on stability analysis of time delay systems which motivated this proposed method

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