A semi-algebraic approach for asymptotic stability analysis

DOI10.1016/j.nahs.2009.04.010zbMath1217.93153OpenAlexW1980496887MaRDI QIDQ1036644

Zhikun She, Bican Xia, Rong Xiao, Zhi Ming Zheng

Publication date: 13 November 2009

Published in: Nonlinear Analysis. Hybrid Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nahs.2009.04.010

zbMATH Keywords

quadratic formasymptotic stabilityLyapunov functionsautonomous systemssemi-algebraic systems

Mathematics Subject Classification ID

Asymptotic stability in control theory (93D20) Algebraic methods (93B25)

Related Items (9)

Exact asymptotic stability analysis and region-of-attraction estimation for nonlinear systems ⋮ Stability analysis of discrete-time switched systems via multi-step multiple Lyapunov-like functions ⋮ FOSSIL ⋮ Discovering polynomial Lyapunov functions for continuous dynamical systems ⋮ Automatic generation of bounds for polynomial systems with application to the Lorenz system ⋮ Parametric Qualitative Analysis of Ordinary Differential Equations: Computer Algebra Methods for Excluding Oscillations (Extended Abstract) (Invited Talk) ⋮ Sufficient and necessary conditions for discrete-time nonlinear switched systems with uniform local exponential stability ⋮ Symbolic computation for the qualitative theory of differential equations ⋮ Special algorithm for stability analysis of multistable biological regulatory systems

Uses Software

• QEPCAD
• Sostools
• RSOLVER
• HSolver

Cites Work

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• On the estimation of asymptotic stability regions: State of the art and new proposals
• The behaviour of optimal Lyapunov functions
• Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
• Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition
• Stability analysis of biological systems with real solution classification
• Hybrid Systems: Computation and Control

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