Computation of continuous and piecewise affine Lyapunov functions for discrete-time systems

Huijuan Li, Sigurður Hafstein, Christopher M. Kellett

Rannsóknarafurð: Framlag til fræðitímaritsGreinritrýni

8 Tilvitnanir (Scopus)

Útdráttur

In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. Given a suitable triangulation of a compact neighbourhood of the origin, a continuous and piecewise affine function can be parameterized by the values at the vertices of the triangulation. If these vertex values satisfy system-dependent linear inequalities, the parameterized function is a Lyapunov function for the system. We propose calculating these vertex values using constructions from two classical converse Lyapunov theorems originally due to Yoshizawa and Massera. Numerical examples are presented to illustrate the proposed approach.

Upprunalegt tungumálEnska
Síður (frá-til)486-511
Síðufjöldi26
FræðitímaritJournal of Difference Equations and Applications
Bindi21
Númer tölublaðs6
DOI
ÚtgáfustaðaÚtgefið - 3 jún. 2015

Athugasemd

Funding Information:
H. Li is supported by the EU Initial Training Network ‘Sensitivity Analysis for Deterministic Controller Design-SADCO’. C.M. Kellett is supported by the Australian Research Council under Future Fellowship [grant number FT1101000746].

Publisher Copyright:
© 2015, Taylor & Francis.

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