scholarly journals Robust Stability and Stabilization for Singular Time-Delay Systems with Linear Fractional Uncertainties: A Strict LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jinxing Lin ◽  
Lina Rong
Keyword(s):  
Robust Stability ◽  
Singular Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Stability And Stabilization ◽  
Delay Dependent ◽  
Robust Stability And Stabilization

This paper is concerned with the problems of delay-dependent robust stability and stabilization for a class of continuous singular systems with time-varying delay in range and parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. In terms of strict linear matrix inequalities (LMIs), delay-range-dependent robust stability criteria for the unforced system are presented. Moreover, a strict LMI design approach is developed such that, when the LMI is feasible, a desired state feedback stabilizing controller can be constructed, which guarantees that, for all admissible uncertainties, the closed-loop dynamics will be regular, impulse free, and robustly asymptotically stable. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.

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.

scholarly journals Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zifan Gao ◽  
Jiaxiu Yang ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
State Variables ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Delay Dependent

This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.

Robust Stabilization of Stochastic Singular Systems with Markovian Switching

2012 ◽  
Vol 591-593 ◽  
pp. 1496-1501
Author(s):  
Yu Cai Ding ◽  
Hong Zhu ◽  
Yu Ping Zhang ◽  
Yong Zeng
Keyword(s):  
Robust Stability ◽  
Singular Systems ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Markovian Jump Parameters ◽  
Stochastic Disturbance ◽  
Stability And Stabilization ◽  
Robust Stability And Stabilization

In this paper, robust stability and stabilization of singular stochastic hybrid systems are investigated. The system under consideration involves parameter uncertainties, Itô-type stochastic disturbance, Markovian jump parameters as well as time-varying delays. The aim of this paper is to design a state controller such that the dynamic system is robust stable. By using the Lyapunov-Krasovskii functional and Itô's differential rule, delay-range-dependent sufficient conditions on robust stability and stabilization are obtained in the form of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results.

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