Stability analysis by contraction principle for impulsive systems with infinite delays

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite. With the help of the notion of stable functions, asymptotic partial stability, exponential partial stability, input-to-state partial stability (ISPS) and integral input-to-state partial stability (iISPS) are considered. Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

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Lyapunov-Based Sufficient Conditions for Nonlinear Impulsive Systems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.219-220.508 ◽

2011 ◽

Vol 219-220 ◽

pp. 508-512

Author(s):

Yong Liang Gao ◽

Xiao Wu Mu

Keyword(s):

Differential Equation ◽

Stability Analysis ◽

Lyapunov Function ◽

Sufficient Conditions ◽

Invariant Set ◽

Positive Definite ◽

Impulsive Systems ◽

Stability Theorems ◽

Sufficient Conditions For Convergence ◽

The Stability

This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. A set of Lyapunov-based sufficient conditions are established for these convergent properties. These results do not require the Lyapunov function to be positive definite. Inequalities relating the righthandside of the differential equation and the Lyapunov function derivative are involved for these results. These inequalities make it possible to deduce properties of the functions and thus leads to sufficient conditions for convergence and stability.

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Stability analysis for a class of random nonlinear impulsive systems

International Journal of Robust and Nonlinear Control ◽

10.1002/rnc.3630 ◽

2016 ◽

Vol 27 (7) ◽

pp. 1171-1193 ◽

Cited By ~ 25

Author(s):

Ticao Jiao ◽

Wei Xing Zheng ◽

Shengyuan Xu

Keyword(s):

Stability Analysis ◽

Impulsive Systems

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Stability in impulsive systems with Markov perturbations in averaging scheme. 2. Averaging principle for impulsive Markov systems and stability analysis based on averaged equations

Cybernetics and Systems Analysis ◽

10.1007/s10559-011-9288-4 ◽

2011 ◽

Vol 47 (1) ◽

pp. 44-54 ◽

Cited By ~ 2

Author(s):

Ye. F. Tsarkov ◽

V. K. Yasinsky ◽

I. V. Malyk

Keyword(s):

Stability Analysis ◽

Averaging Principle ◽

Impulsive Systems ◽

Markov Systems ◽

Averaged Equations

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Semistability of Nonlinear Impulsive Systems with Delays

Mathematical Problems in Engineering ◽

10.1155/2012/260236 ◽

2012 ◽

Vol 2012 ◽

pp. 1-10

Author(s):

Xiaowu Mu ◽

Yongliang Gao

Keyword(s):

Stability Analysis ◽

Hybrid System ◽

Lyapunov Functional ◽

Sufficient Conditions ◽

Impulsive Systems ◽

Stability Properties ◽

System Energy ◽

The Stability ◽

Storage Energy

This paper is concerned with the stability analysis and semistability theorems for delay impulsive systems having a continuum of equilibria. We relate stability and semistability to the classical concepts of system storage functions to impulsive systems providing a generalized hybrid system energy interpretation in terms of storage energy. We show a set of Lyapunov-based sufficient conditions for establishing these stability properties. These make it possible to deduce properties of the Lyapunov functional and thus lead to sufficient conditions for stability and semistability. Our proposed results are evaluated using an illustrative example to show their effectiveness.

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