Construction of continuous and piecewise affine Lyapunov functions via a finite-time converse. Issue 18 (2016)

• Record Type: Journal Article
• Authors: Steentjes, Tom R.V.; Doban, Alina I.; Lazar, Mircea
• Is Part Of: IFAC-PapersOnLine. Volume 49:Issue 18(2016)
• Page Start: 13
• Page End: 18
• Publication Date: 2016
• Subjects: Lyapunov methods -- computational methods -- stability domains -- nonlinear systems -- numerical algorithms -- stability analysis; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2016.10.132
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: A novel numerical Massera-type approach for the computation of Lyapunov functions (LFs) for nonlinear continuous-time systems is presented. The construction is enabled by verifying a finite-time decrease condition for a candidate function, which is allowed to be any K ∞ function of the norm of the state, and applying a converse Lyapunov theorem. In the construction we make use of approximated system trajectories and we obtain a continuous and piecewise affine (CPA) LF. By optimization, the obtained CPA LF is verified and an estimate of the domain of attraction is obtained. Several examples are presented for illustration and demonstration of the effectiveness of the proposed approach.