Robust Stability for Nonlinear Systems with Time-Varying Delay and Uncertainties via theH∞Quasi-Sliding Mode Control

This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on theH∞theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI) optimization technique, theH∞quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance). The effectiveness and accuracy of the proposed methods are shown in numerical simulations.

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On robust stability for uncertain neutral systems with non-differentiable interval time-varying discrete delay and nonlinear perturbations

Asian-European Journal of Mathematics ◽

10.1142/s1793557118500079 ◽

2017 ◽

Vol 11 (01) ◽

pp. 1850007 ◽

Cited By ~ 3

Author(s):

Peerapongpat Singkibud ◽

Kanit Mukdasai

Keyword(s):

Robust Stability ◽

Linear Matrix ◽

Time Varying ◽

Nonlinear Perturbations ◽

Neutral Systems ◽

Interval Time ◽

Time Varying Delay ◽

Robust Stability Analysis ◽

Discrete Interval ◽

Varying Delay

In this paper, we investigate the problem of delay-range-dependent robust stability analysis for uncertain neutral systems with interval time-varying delays and nonlinear perturbations. The restriction on the derivative of the discrete interval time-varying delay is removed. By applying the augmented Lyapunov–Krasovskii functional approach, new improved integral inequalities, descriptor model transformation, Leibniz–Newton formula and utilization of zero equation, new delay-range-dependent robust stability criteria are derived in terms of linear matrix inequalities (LMIs) for the considered systems. Numerical examples have shown to illustrate the significant improvement on the conservatism of the delay upper bound over some reported results.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.461.633 ◽

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.

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Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

Mathematical Problems in Engineering ◽

10.1155/2008/875609 ◽

2008 ◽

Vol 2008 ◽

pp. 1-15 ◽

Cited By ~ 17

Author(s):

Valter J. S. Leite ◽

Márcio F. Miranda

Keyword(s):

Robust Stability ◽

Discrete Time ◽

Robust Stabilization ◽

Linear Matrix ◽

Time Varying ◽

Time Varying Delay ◽

Discrete Time Systems ◽

Robust Stability Analysis ◽

Time Systems ◽

Varying Delay

Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.

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Robust stability criterion for uncertain stochastic systems with time-varying delay via sliding mode control

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.03.120 ◽

2014 ◽

Vol 238 ◽

pp. 70-81 ◽

Cited By ~ 14

Author(s):

Yude Ji ◽

Jiqing Qiu

Keyword(s):

Sliding Mode Control ◽

Robust Stability ◽

Stability Criterion ◽

Stochastic Systems ◽

Sliding Mode ◽

Time Varying ◽

Time Varying Delay ◽

Mode Control ◽

Varying Delay

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H∞Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

Mathematical Problems in Engineering ◽

10.1155/2015/473165 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

C. Emharuethai ◽

P. Niamsup

Keyword(s):

Nonlinear System ◽

State Feedback ◽

Sufficient Conditions ◽

State Feedback Control ◽

Linear Matrix ◽

Time Varying ◽

Matrix Inequalities ◽

Numerical Examples ◽

Time Varying Delay ◽

Varying Delay

H∞control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality.H∞controller is designed via memoryless state feedback control and new sufficient conditions for the existence of theH∞state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

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Robust Stability Criteria for Uncertain Neutral Systems with Interval Nondifferentiable Time-Varying Delay and Nonlinear Perturbations

Journal of Applied Mathematics ◽

10.1155/2011/138912 ◽

2011 ◽

Vol 2011 ◽

pp. 1-20 ◽

Cited By ~ 2

Author(s):

W. Weera ◽

P. Niamsup

Keyword(s):

Robust Stability ◽

Linear Matrix ◽

Fast Time ◽

Time Varying ◽

Nonlinear Perturbations ◽

Stability Criteria ◽

Neutral Systems ◽

Time Varying Delay ◽

Delay Dependent ◽

Varying Delay

We study the robust stability criteria for uncertain neutral systems with interval time-varying delays and time-varying nonlinear perturbations simultaneously. The constraint on the derivative of the time-varying delay is not required, which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.

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Novel Approach to Robust Stability Criteria of Uncertain System with Time-Varying Delay

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.631-632.1189 ◽

2013 ◽

Vol 631-632 ◽

pp. 1189-1194

Author(s):

Chao Deng ◽

Zhao Di Xu ◽

Yu Bai ◽

Xin Yuan Wang

Keyword(s):

Linear Matrix Inequality ◽

Robust Stability ◽

Uncertain System ◽

Linear Matrix ◽

Convexity Property ◽

Time Varying ◽

Matrix Inequality ◽

Stability Criteria ◽

Time Varying Delay ◽

Varying Delay

This paper considers the robust stability criteria of uncertain system with time-varying delay. Firstly, by exploiting a new Lyapunov function that optimizes the segment of time delay and using the convexity property and free-weight method of the Linear Matrix Inequality, delay-dependent stability condition can be obtained for the asymptotical stability of the nominal system. Secondly, basing on the obtained condition, the corresponding linear matrix inequality can be obtained for the uncertain system. Finally, an example is given to demostrate the effectiveness and the merit of the proposed method.

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IMPROVED ROBUST STABILITY CRITERION FOR UNCERTAIN CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAY

Modern Physics Letters B ◽

10.1142/s0217984910022615 ◽

2010 ◽

Vol 24 (04n05) ◽

pp. 503-511 ◽

Cited By ~ 1

Author(s):

S. M. LEE

Keyword(s):

Neural Networks ◽

Robust Stability ◽

Stability Criterion ◽

Nonlinear Function ◽

Cellular Neural Networks ◽

Linear Matrix ◽

Time Varying ◽

Time Varying Delay ◽

Robust Stability Analysis ◽

Varying Delay

In this paper, we propose a new robust stability analysis method for uncertain cellular neural networks with time-varying delay. The proposed stability criterion is based on the Lyapunov function with sector bounded nonlinear function. The sufficient condition for the stability is derived in terms of LMI (linear matrix inequality). Numerical examples show the effectiveness of the proposed method.

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Sliding Mode Control Based on Novel Nonlinear Sliding Surface for a Class of Time-Varying Delay Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.615.375 ◽

2014 ◽

Vol 615 ◽

pp. 375-381

Author(s):

Qi Feng Ren ◽

Cun Che Gao ◽

Shu Hui Bi

Keyword(s):

Sliding Mode Control ◽

Sliding Mode ◽

Sufficient Conditions ◽

Delay Systems ◽

Linear Matrix ◽

Time Varying ◽

Sliding Surface ◽

Time Varying Delay ◽

Mode Control ◽

Varying Delay

The sliding mode control (SMC) design is discussed for a class of time-varying delay systems which is delay-range-dependent and rate-range-dependent. A novel time-varying nonlinear sliding surface is employed. The choice of nonlinear sliding surface is to change the state matrix of sliding mode system, which can combine the advantages of different conventional linear sliding surfaces. Thus the better transient qualities of system states, i.e., quicker response and smaller overshoot, can be achieved. The sufficient conditions ensuring the asymptotic stability of sliding mode are derived in terms of linear matrix inequalities. The algorithms deciding unknown parameters of the nonlinear sliding surface and the corresponding sliding mode controller are also presented. Finally, A numerical example is given to illustrate the effectiveness of the result here.

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