New Stabilization for Dynamical System with Two Additive Time-Varying Delays

This paper provides a new delay-dependent stabilization criterion for systems with two additive time-varying delays. The novel functional is constructed, a tighter upper bound of the derivative of the Lyapunov functional is obtained. These results have advantages over some existing ones because the combination of the delay decomposition technique and the reciprocally convex approach. Two examples are provided to demonstrate the less conservatism and effectiveness of the results in this paper.

Download Full-text

Novel Stabilization for Systems with Two Additive Time-Varying Delays

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.610.523 ◽

2014 ◽

Vol 610 ◽

pp. 523-533

Author(s):

Liang Lin Xiong ◽

Di Li ◽

Yan Fang Zuo

Keyword(s):

Upper Bound ◽

Lyapunov Functional ◽

Time Varying ◽

The Novel ◽

Delay Dependent ◽

Delay Decomposition ◽

Reciprocally Convex Approach

This paper provides a new delay-dependent stabilization criterion for systems with two additive time-varying delays. The novel functional is constructed, a tighter upper bound of the derivative of the Lyapunov functional is obtained. These results have advantages over some existing ones in that the skillfully combination of the delay decomposition and reciprocally convex approach. Two examples are provided to demonstrate the less conservatism and effectiveness of the results in this paper.

Download Full-text

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4052041 ◽

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.

Download Full-text

Delay-dependent stability analysis for discrete-time switched linear systems with parametric uncertainties

Journal of Vibration and Control ◽

10.1177/1077546317739735 ◽

2017 ◽

Vol 24 (20) ◽

pp. 4921-4930 ◽

Cited By ~ 12

Author(s):

Nasrollah Azam Baleghi ◽

Mohammad Hossein Shafiei

Keyword(s):

Stability Analysis ◽

Time Delay ◽

Discrete Time ◽

Upper Bound ◽

Sufficient Conditions ◽

Switched System ◽

Parametric Uncertainties ◽

Time Varying ◽

Delay Dependent ◽

Delay Dependent Stability

This paper studies the delay-dependent stability conditions for time-delay discrete-time switched systems. In the considered switched system, there are uncertain terms in each subsystem due to affine parametric uncertainties. Additionally, each subsystem has a time-varying state delay which adds more complexity to the stability analysis. Based on the Lyapunov functional approach, the sufficient conditions are extracted to determine the admissible upper bound of the time-varying delay for guaranteed stability. Furthermore, a class of switching signals is identified to guarantee the exponential stability of the uncertain time-delay switched system. The main advantage of the suggested switching signals is its independency to the uncertainties. Furthermore, these signals are only constrained by a determined average dwell time (may be chosen arbitrarily). Finally, a numerical example is provided to demonstrate the efficiency of the proposed method and also the reduction of conservatism in finding the admissible upper bound of time-delay in comparison with other stability analysis approaches.

Download Full-text

New Delay-Dependent Stability Conditions for Time-Varying Delay Systems

Mathematical Problems in Engineering ◽

10.1155/2013/360924 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Wei Qian ◽

Hamid Reza Karimi

Keyword(s):

Delay Systems ◽

Time Varying ◽

Stability Criteria ◽

Time Varying Delay ◽

Decision Variables ◽

Delay Dependent ◽

Delay Dependent Stability ◽

Varying Delay ◽

Theoretical Results ◽

Reciprocally Convex Approach

This paper addresses the delay-dependent stability for systems with time-varying delay. First, by taking multi-integral terms into consideration, new Lyapunov-Krasovskii functional is defined. Second, in order to reduce the computational complexity of the main results, reciprocally convex approach and some special transformations are introduced, and new delay-dependent stability criteria are proposed, which are less conservative and have less decision variables than some previous results. Finally, two well-known examples are given to illustrate the correctness and advantage of our theoretical results.

Download Full-text

Delayed-Decomposition Approach for Absolute Stability of Neutral-Type Lurie Control Systems With Time-Varying Delays

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4029720 ◽

2015 ◽

Vol 137 (8) ◽

Cited By ~ 2

Author(s):

Pin-Lin Liu

Keyword(s):

Control Systems ◽

Lyapunov Functional ◽

Absolute Stability ◽

Neutral Type ◽

Upper Bounds ◽

Linear Matrix ◽

Time Varying ◽

Matrix Inequalities ◽

Decomposition Approach ◽

Delay Dependent

The problem of absolute stability for a class of neutral-type Lurie control system with nonlinearity located in an infinite sector and in a finite one is investigated in this paper. Based on the delayed-decomposition approach (DDA), a new augmented Lyapunov functional is constructed and the delay dependent conditions for asymptotic stability are derived by applying an integral inequality approach (IIA) in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

Download Full-text