Computation of local ISS Lyapunov functions with low gains via linear programming | Zendy

Huijuan Li | Zendy; Robert Baier | Zendy; Lars Grüne | Zendy; Sigurður Hafstein | Zendy; Fabian Wirth | Zendy

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Computation of local ISS Lyapunov functions with low gains via linear programming

Author(s) -

Huijuan Li,

Robert Baier,

Lars Grüne,

Sigurður Hafstein,

Fabian Wirth

Publication year - 2015

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2015.20.2477

Subject(s) - lyapunov function , lyapunov optimization , lipschitz continuity , piecewise linear function , mathematics , linear programming , affine transformation , computation , state (computer science) , grid , mathematical optimization , state space , lyapunov redesign , algorithm , nonlinear system , mathematical analysis , statistics , physics , geometry , quantum mechanics , pure mathematics

In this paper, we present a numerical algorithm for computing ISS Lyapunov functions for continuous-time systems which are input-to-state stable (ISS) on compact subsets of the state space. The algorithm relies on a linear programming problem and computes a continuous piecewise ane ISS Lyapunov function on a simplicial grid covering the given compact set excluding a small neighborhood of the origin. The objective of the linear programming problem is to minimize the gain. We show that for every ISS system with a locally Lipschitz right-hand side our algorithm is in principle able to deliver an ISS Lyapunov function. For C2 right-hand sides a more ecient algorithm is proposed.

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