Switching Design for the Asymptotic Stability and Stabilization of Nonlinear Uncertain Stochastic Discrete-time Systems

2013 ◽  
Vol 14 (1) ◽  
pp. 33-44
Author(s):  
Grienggrai Rajchakit
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Discrete Time Delay ◽  
Stability And Stabilization

Abstract This paper is concerned with asymptotic stability and stabilization of nonlinear uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability and stabilization for the nonlinear uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

A SWITCHING RULE FOR THE ASYMPTOTIC STABILITY OF UNCERTAIN DISCRETE-TIME SYSTEMS

2011 ◽  
Vol 08 (03) ◽  
pp. 255-261 ◽  
Author(s):  
K. RATCHAGIT
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Uncertain System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Switching Rule ◽  
Discrete Time Delay ◽  
Time Systems

This paper is concerned with asymptotic stability of uncertain switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability for the uncertain system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

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.

scholarly journals Robustl2-l∞Filtering for Discrete-Time Delay Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chengming Yang ◽  
Zhandong Yu ◽  
Pinchao Wang ◽  
Zhen Yu ◽  
Hamid Reza Karimi ◽  
...  
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Estimation Error ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Time Varying Delay ◽  
Discrete Time Delay ◽  
Error System ◽  
Varying Delay

The problem of robustl2-l∞filtering for discrete-time system with interval time-varying delay and uncertainty is investigated, where the time delay and uncertainty considered are varying in a given interval and norm-bounded, respectively. The filtering problem based on thel2-l∞performance is to design a filter such that the filtering error system is asymptotically stable with minimizing the peak value of the estimation error for all possible bounded energy disturbances. Firstly, sufficientl2-l∞performance analysis condition is established in terms of linear matrix inequalities (LMIs) for discrete-time delay systems by utilizing reciprocally convex approach. Then a less conservative result is obtained by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, the robustl2-l∞filter is designed for systems with time-varying delay and uncertainty. Finally, a numerical example is given to demonstrate the effectiveness of the filter design method.

scholarly journals On the asymptotic stability of linear discrete time-delay systems: The Lyapunov approach

2006 ◽  
Vol 60 (3-4) ◽  
pp. 78-81
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic ◽  
Ilija Mladenovic
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Discrete Delay ◽  
Lyapunov Approach ◽  
Numerical Example ◽  
Discrete Time Delay ◽  
The Stability

New conditions for the stability of discrete delay systems of the form x (k+1) = Arjx (k) + Aix (k-h) are presented in the paper. These new delay-independent conditions were derived using an approach based on the second Lyapunov's method. These results are less conservative than some in the existing literature. A numerical example was worked out to show the applicability of the derived results.

scholarly journals On the Asymptotic Stability of Linear Discrete Time Delay Systems

Volume 1 ◽  
2004 ◽  
Author(s):  
S. B. Stojanovic ◽  
D. Lj. Debeljkovic
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Numerical Example ◽  
Discrete Time Delay ◽  
Time Invariant ◽  
Working Out

This paper extends some of the basic results in the area of Lyapunov (asymptotic) to linear, discrete, time invariant time-delay systems. These results are given in the form of only sufficient conditions and represent other generalisation of some previous ones or completely new results. In the latter case it is easy to show that, in the most cases, these results are less conservative then those in existing literature. A numerical example has been working out to show the applicability of results derived. To the best knowledge of the authors, such results have not yet been reported.

Robust Fault-Tolerant Control for a Class of Uncertain Discrete Time-Delay Systems

2012 ◽  
Vol 532-533 ◽  
pp. 521-526
Author(s):  
De Gong Zhao ◽  
Yue Chao Ma
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequality ◽  
Fault Tolerant ◽  
Fault Tolerant Control ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Actuator Failures ◽  
Discrete Time Delay

The problem of robust fault-tolerant control for the uncertain time-delay system with state and control delays is studied.The considered system has sensor or actuator failures.Based on Lyapunov stability theory and linear matrix inequality(LMI),a method of robust fault-tolerant against sensor or actuator failures for uncertain system was proposed via memoryless feedback control law.The sufficient for the closed-loop system possessing integrity against sensor or actuator failures are given.At the same time,the controller design method is the linear matrix inequality(LMI).Finally,the numerical example and simulations demonstrate the validity of the proposed method.

scholarly journals Observer-Based Bounded Control for Discrete Time-Delay Uncertain Nonlinear Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Bei Wu ◽  
Mou Chen ◽  
Xiaoming Chen
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Disturbance Observer ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
State Estimator ◽  
Bounded Control ◽  
Discrete Time Delay ◽  
Unknown Disturbance

A bounded controller is proposed for a class of uncertain discrete time-delay systems with nonlinearity and disturbance based on state estimator and disturbance observer technique. A state estimator is developed to estimate the unmeasured system state vector. Suppose that the disturbance is generated by an exogenous system; a disturbance observer is designed to estimate the unknown disturbance. The parameters of the state estimator and the disturbance observer are calculated by solving linear matrix inequalities (LMIs). By applying the outputs of the state estimator and the disturbance observer, the sufficient condition for the existence of the bounded controller is derived based on an appropriate Lyapunov function candidate. Under the developed bounded controller, the stability of the closed-loop system can be guaranteed. Simulation examples are provided to show the effectiveness of the proposed bounded control scheme.

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.

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