scholarly journals Delay-Dependent Stability Analysis for Uncertain Switched Time-Delay Systems Using Average Dwell Time

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yangming Zhang ◽  
Peng Yan
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Exponential Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Delay Dependent

We are concerned with the stability problem for linear discrete-time switched systems with time delays. The problem is solved by using multiple Lyapunov functions to develop constructive tools for the exponential stability analysis of the switched time-delay system. Furthermore, the uncertainties of the switched systems are also taken into consideration. Sufficient delay-dependent conditions are derived in terms of the average dwell time for the exponential stability based on linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

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.

Parameterization approach to stability and feedback stabilization of linear time-delay systems

2009 ◽  
Vol 223 (7) ◽  
pp. 929-939
Author(s):  
M S Mahmoud ◽  
A Ismail ◽  
F M Al-Sunni
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Delay System ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Systematic Analysis ◽  
Feedback Scheme ◽  
Delay Dependent

This paper develops a new parameterized approach to the problems of delay-dependent analysis and feedback stabilization for a class of linear continuous-time systems with time-varying delays. An appropriate Lyapunov-Krasovskii functional is constructed to exhibit the delay-dependent dynamics. The construction guarantees avoiding bounding methods and effectively deploying injecting parametrized variables to facilitate systematic analysis. Delay-dependent stability provides a characterization of linear matrix inequalities (LMIs)-based conditions under which the linear time-delay system is asymptotically stable with a γ-level £2 gain. By delay-dependent stabilization, a state-feedback scheme is designed to guarantee that the closed-loop switched system enjoys the delay-dependent asymptotic stability with a prescribed γ-level £2 gain. It is established that the methodology provides the least conservatism in comparison with other published methods. Extension to systems with convex-bounded parameter uncertainties in all system matrices is also provided. All the developed results are tested on representative examples.

scholarly journals A UNIFIED APPROACH TO EXPONENTIAL STABILITY ANALYSIS FOR A GENERAL CLASS OF SWITCHED TIME-DELAY LINEAR SYSTEMS

2021 ◽  
Vol 37 (3) ◽  
pp. 339-350
Author(s):  
Nguyen Khoa Son ◽  
Ngoc Van Le
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Linear Systems ◽  
Dwell Time ◽  
Functional Differential Equations ◽  
Average Dwell Time ◽  
Unified Approach ◽  
Arbitrary Switching ◽  
Functional Differential ◽  
Delay Dependent

This paper proposes a unified approach to study global  exponential stability for  a class of switched time-delay linear  systems described by general linear functional differential equations. Several new delay-dependent criteria of exponential stability are established for this class of systems, under arbitrary switching which satisfies some assumptions on the minimum dwell time or the average dwell time. As particular cases, the obtained results are shown to include and improve many previously known results. An example is given to illustrate the proposed method.

scholarly journals Stability Analysis of State Saturation 2D Discrete Time-Delay Systems Based on F-M Model

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Dongyan Chen ◽  
Hui Yu
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Discrete Time ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Discrete Time Delay ◽  
Discrete Lyapunov Functional ◽  
Delay Dependent ◽  
State Saturation

The problem of stability analysis is investigated for a class of state saturation two-dimensional (2D) discrete time-delay systems described by the Fornasini-Marchesini (F-M) model. The delay is allowed to be a bounded time-varying function. By constructing the delay-dependent 2D discrete Lyapunov functional and introducing a nonnegative scalarβ, a sufficient condition is proposed to guarantee the global asymptotic stability of the addressed systems. Subsequently, the criterion is converted into the linear matrix inequalities (LMIs) which can be easily tested by using the standard numerical software. Finally, two numerical examples are given to show the effectiveness of the proposed stability criterion.

scholarly journals New delay-dependent observer-based control for uncertain stochastic time-delay systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiu-feng Miao ◽  
Long-suo Li
Keyword(s):  
Time Delay ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Noise Disturbances ◽  
System States ◽  
Delay Dependent ◽  
Stochastic Time

AbstractThis paper considers the problem of estimating the state vector of uncertain stochastic time-delay systems, while the system states are unmeasured. The system under study involves parameter uncertainties, noise disturbances and time delay, and they are dependent on the state. Based on the Lyapunov–Krasovskii functional approach, we present a delay-dependent condition for the existence of a state observer in terms of a linear matrix inequality. A numerical example is exploited to show the validity of the results obtained.

Stabilizing Gain Regions of PID Controller for Time Delay Systems

2013 ◽  
Vol 313-314 ◽  
pp. 432-437
Author(s):  
Fu Min Peng ◽  
Bin Fang
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Pid Controller ◽  
Delay System ◽  
Nyquist Plot ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Frequency Range ◽  
Time Delay System ◽  
Key Points

Based on the inverse Nyquist plot, this paper proposes a method to determine stabilizing gain regions of PID controller for time delay systems. According to the frequency characteristic of the inverse Nyquist plot, it is confirmed that the frequency range is used for stability analysis, and the abscissas of two kind key points are obtained in this range. PID gain is divided into several regions by abscissas of key points. Using an inference and two theorems presented in the paper, the stabilizing PID gain regions are determined by the number of intersections of the inverse Nyquist plot and the vertical line in the frequency range. This method is simple and convenient. It can solve the problem of getting the stabilizing gain regions of PID controller for time delay system.

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