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Estimation of LISS(local input-to-state stability) properties for nonlinear systems

Science China(Technological Sciences) 2010年第4期53卷 909-917页

作者： WU ShengYu,MEI ShengWei & ZHANG XueMin state Key Laboratory of Power Systems,Department of Electrical Engineering,Tsinghua University,Beijing 100084,China state Key Laboratory of Power Systems Department of Electrical Engineering Tsinghua University Beijing China

Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI) methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.

关键词： locally input-to-state stability LISS-Lyapunov function linear matrix inequality

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Partial stability analysis of nonlinear time-varying impulsive systems

引用

International Journal of Biomathematics 2019年第6期12卷 73-98页

作者： Boulbaba Ghanmi Faculty of Sciences of Gafsa University of GafsaSidi Ahmed Zarroug 2112GafsaTunisia

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.

关键词： Nonlinear impulsive systems partial stability piecewise continuous scalar functions indefinite Lyapunov function input-to-state partial stability(ISPS) integral input-to-state partial stability(iISPS).

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