Computation of local ISS Lyapunov functions with low gains via linear programming. (English) Zbl 1366.37146

Summary: 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 affine 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 \(C^2\) right-hand sides a more efficient algorithm is proposed.


37M99 Approximation methods and numerical treatment of dynamical systems
93D09 Robust stability
93D30 Lyapunov and storage functions
90C05 Linear programming
93D25 Input-output approaches in control theory
90C90 Applications of mathematical programming
Full Text: DOI


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