Estimating the robust domain of attraction for non-smooth systems using an interval Lyapunov equation

DOI10.1016/j.automatica.2018.03.036zbMath1415.93080OpenAlexW2732979857WikidataQ128832545 ScholiaQ128832545MaRDI QIDQ1737666

Alexandre Goldsztejn, Gilles Chabert

Publication date: 24 April 2019

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2018.03.036

zbMATH Keywords

Lyapunov functionnonlinear systemsinterval analysisdomain of attractionexponentially stable fixed-point

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Control/observation systems with incomplete information (93C41) Lyapunov and storage functions (93D30) Linearizations (93B18) Asymptotic stability in control theory (93D20)

Related Items (4)

On norm-based estimations for domains of attraction in nonlinear time-delay systems ⋮ Inner-estimating domains of attraction for discrete-time non-polynomial systems with piecewise difference inclusions ⋮ Data-driven robust stabilization with robust domain of attraction estimate for nonlinear discrete-time systems ⋮ Inner-approximating domains of attraction for discrete-time switched systems via multi-step multiple Lyapunov-like functions

Uses Software

• INTLAB
• IBEX
• SMRSOFT

Cites Work

• Linear and parabolic relaxations for quadratic constraints
• Upper bounding in inner regions for global optimization under inequality constraints
• Domain of attraction. Analysis and control via SOS programming.
• Contractor programming
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• Estimating the domain of attraction for non-polynomial systems via LMI optimizations
• A hybrid discretization algorithm with guaranteed feasibility for the global solution of semi-infinite programs
• Revised CPA method to compute Lyapunov functions for nonlinear systems
• Domain-of-attraction estimation for uncertain non-polynomial systems
• Conjugate Lyapunov functions for saturated linear systems
• Connecting Orbits for a Singular Nonautonomous Real Ginzburg--Landau Type Equation
• Guaranteed estimates of the domain of attraction for a class of hybrid systems
• Rigorous Enclosures of Ellipsoids and Directed Cholesky Factorizations
• Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions
• Rigorous Error Bounds for the Optimal Value in Semidefinite Programming
• Interval Methods for Systems of Equations
• Positive Definiteness and Stability of Interval Matrices
• Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition
• Expansion and estimation of the range of nonlinear functions
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