Homogeneous Lyapunov Functions: From Converse Design to Numerical Implementation | Zendy

Denis Efimov | Zendy; Rosane Ushirobira | Zendy; Jaime A. Moreno | Zendy; Wilfrid Perruquetti | Zendy

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Homogeneous Lyapunov Functions: From Converse Design to Numerical Implementation

Author(s) -

Denis Efimov,

Rosane Ushirobira,

Jaime A. Moreno,

Wilfrid Perruquetti

Publication year - 2018

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/17m113753x

Subject(s) - mathematics , lyapunov function , converse , homogeneous , infimum and supremum , homogeneity (statistics) , lyapunov equation , homogeneous function , mathematical analysis , lyapunov redesign , stability theory , function (biology) , nonlinear system , combinatorics , geometry , statistics , physics , quantum mechanics , evolutionary biology , biology

The problem of the synthesis of a homogeneous Lyapunov function for an asymptotically stable homogeneous system is studied. First, for systems with nonnegative degree of homogeneity, several expressions of homogeneous Lyapunov functions are derived, which depend explicitly on the supremum or the integral (over finite or infinite intervals of time) of the system solutions. Second, a numeric procedure is proposed, which ensures the construction of a homogeneous Lyapunov function. The analytical results are illustrated by simulations.

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