Exponential Delay Dependent Stabilization for Time-Varying Delay Systems With Saturating Actuator

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Time Delay ◽  
Design Method ◽  
Delay System ◽  
Rate Of Change ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper deals with the stabilization criteria for a class of time-varying delay systems with saturating actuator. Based on the Lyapunov–Krasovskii functional combining with linear matrix inequality techniques and Leibniz–Newton formula, delay-dependent stabilization criteria are derived using a state feedback controller. We also consider efficient convex optimization algorithms to the time-varying delay system with saturating actuator case: the maximal bound on the time delay such that the prescribed level of operation range and imposed exponential stability requirements are still preserved. The value of the time-delay as well as its rate of change are taken into account in the design method presented and further permit us to reduce the conservativeness of the approach. The results have been illustrated by given numerical examples. These results are shown to be less conservative than those reported in the literature.

Conservativeness Judgement of Controller for Systems with Time-Varying Delay

2012 ◽  
Vol 249-250 ◽  
pp. 1173-1179
Author(s):  
Jiu Ying Deng ◽  
Hui Fei Deng ◽  
Jian Bin Xiong ◽  
Qin Ruo Wang
Keyword(s):  
Delay System ◽  
Delay Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Optimization Approach ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

The conservatism of asymptotic stability conditions is considered in terms of linear matrix inequalities for time-varying delay systems. The conservative index is defined to evaluate the conservativeness for both delay-dependent and delay-independent stability conditions. The general results on performance analysis are presented based on descriptor system approach. The conservativeness index is defined for time-varying delay system. The optimization approach is given to obtain the upper delay and rational performances for the state-feedback controller of time-delay systems. Experimental results verify the effectiveness of the new method.

scholarly journals A Novel Approach toH∞Control Design for Linear Neutral Time-Delay Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongwei Xia ◽  
Pingping Zhao ◽  
Li Li ◽  
Aiguo Wu ◽  
Guangcheng Ma
Keyword(s):  
Design Method ◽  
Delay Systems ◽  
Linear Matrix ◽  
Neutral Systems ◽  
Time Varying Delay ◽  
Bounded Real Lemma ◽  
Novel Approach ◽  
Delay Dependent ◽  
Delay Partitioning ◽  
Varying Delay

This paper is concerned with the problem ofH∞control of linear neutral systems with time-varying delay. Firstly, by applying a novel Lyapunov-Krasovskii functional which is constructed with the idea of delay partitioning approach, appropriate free-weighting matrices, an improved delay-dependent bounded real lemma (BRL) for neutral systems is established. By using the obtained BRL, a delay-dependent sufficient condition for the existence of a state-feedback controller, which ensures asymptotic stability and a prescribedH∞performance level of the corresponding closed-loop system, is formulated in terms of linear matrix inequalities. Some numerical examples are given to illustrate the effectiveness of the proposed design method.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Tiejun Li ◽  
Junkang Tian
Keyword(s):  
Stability Criterion ◽  
Convex Polyhedron ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Polyhedron Method ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Observer-Based Stabilization of Linear Discrete Time-Varying Delay Systems

2021 ◽  
Author(s):  
Venkatesh Modala ◽  
Sourav Patra ◽  
Goshaidas Ray
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Summation Inequality ◽  
Delay Dependent

Abstract This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov-Krasovskii (LK) functional to derive a delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus, ensure global asymptotic stability in presence of any time delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

New Delay-Dependent Robust Stability Criterion for Uncertain Stochastic Systems with Time-Varying Delays

2012 ◽  
Vol 461 ◽  
pp. 633-636
Author(s):  
Cheng Wang
Keyword(s):  
Robust Stability ◽  
Stability Criterion ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

The problem of delay-dependent robust stability of uncertain stochastic systems with time-varying delay is discussed in this paper. Based on the Lyapunov-Krasovskii theory and free-weighting matrix technique, new delay-dependent stability criterion is presented. The criterion is in terms of linear matrix inequality (LMI) which can be solved by various available algorithms.

scholarly journals Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 447 ◽  
Author(s):  
Yanli Ruan ◽  
Tianmin Huang
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Delay System ◽  
Time Varying ◽  
Time Delay System ◽  
Time Varying Delay ◽  
Time Control ◽  
Exogenous Disturbance ◽  
Varying Delay

This paper is concerned with the problem of finite-time control for nonlinear systems with time-varying delay and exogenous disturbance, which can be represented by a Takagi–Sugeno (T-S) fuzzy model. First, by constructing a novel augmented Lyapunov–Krasovskii functional involving several symmetric positive definite matrices, a new delay-dependent finite-time boundedness criterion is established for the considered T-S fuzzy time-delay system by employing an improved reciprocally convex combination inequality. Then, a memory state feedback controller is designed to guarantee the finite-time boundness of the closed-loop T-S fuzzy time-delay system, which is in the framework of linear matrix inequalities (LMIs). Finally, the effectiveness and merits of the proposed results are shown by a numerical example.

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