A new Lyapunov function for stability of time-varying nonlinear perturbed systems

In this paper we propose sufficient conditions for the robust stability of time-invariant uncertain piecewise-linear systems using homogeneous polynomial Lyapunov functions. The proposed conditions are expressed in terms of linear matrix inequalities, which can be numerically determined. We solve the stabilization of piecewise uncertain linear control systems by using state piecewise-linear feedback. We propose an illustrative example to show the efficiency of the proposed approach.

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“…We conclude that V (x, α) is a PHPLF for system (1) and the origin of the system is robustly stable. Thus the proof is completed.…”

Section: Theoremmentioning

confidence: 74%

“…Recently, a new Lyapunov function was constructed to study the stability of time-varying nonlinear perturbed systems [1]. A typical perturbation is the dependence of unknown parameters.…”

Section: Introductionmentioning

confidence: 99%

Robust stability of uncertain piecewise-linear systems: LMI approach

Benabdallah¹,

Hammami

Kallel

2010

Nonlinear Dyn

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“…For example, those results can be found in [4][5][6][7][8][9][10] and the references cited therein. It is well known that if both a(t) and b(t) are periodic functions (or constants), then the equilibrium x = x = 0 of (E) is asymptotically stable if and only if it is uniformly asymptotically stable.…”

Section: Introductionmentioning

confidence: 82%

Non-uniform asymptotic stability for the damped linear oscillator

Onitsuka¹

2010

Nonlinear Analysis: Theory, Methods & Applications

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“…In this work, we have treated the case where the system presents a perturbation term, which could result from errors in modeling the nonlinear system aging of parameters, or uncertainties and disturbances which exist in any realistic problems [2,4,17]. We do not know the term perturbation, but we know some information about it, like knowing an upper bound on it.…”

Section: Introductionmentioning

confidence: 99%

State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

et al. 2015

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In this paper, the problem of stabilization of a specific class of nonlinear dynamical system with unknown, bounded, time-varying delay is considered. A new stabilizing control law guarantees the practical stability of the system. A modified extended control law leads to the exponential stability. A Lyapunov function is chosen, and sufficient assumptions are provided in order to prove the stability of the proposed feedback system. Simulation results are addressed to show the effectiveness of the suggested control design method.

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A new Lyapunov function for stability of time-varying nonlinear perturbed systems

Cited by 45 publications

References 11 publications

Robust stability of uncertain piecewise-linear systems: LMI approach

Robust stability of uncertain piecewise-linear systems: LMI approach

Non-uniform asymptotic stability for the damped linear oscillator

State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

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