Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems

Construction of a local and global Lyapunov function for discrete dynamical systems using radial basis functions

“…In a similar approach to Zubov's method, Vannelli and Vidyasagar [17] use a rational function as Lyapunov function candidate and present an algorithm to obtain a maximal Lyapunov function in the case that f is analytic. In Camilli et al [2], Zubov's method was extended to control problems in order to determine the robust domain of attraction.…”

A novel LMI-based optimization algorithm for the guaranteed estimation of the domain of attraction using rational Lyapunov functions

“…In Section 4 we recall some results from the mathematical theory of moments proved by Lasserre in [38] and show how they can be used to estimate the DOA for polynomial dynamical systems using polynomial Lyapunov functions. In Section 5 we shortly review the maximal Lyapunov functions and their rational approximations introduced by Vannelli and Vidysagar in [16]. In Section 6 we present a new LMI-based method for estimating the DOA using rational Lyapunov functions.…”

“…The investigation of the stability of such nonlinear dynamical systems leads to the inevitable task; having determined its equilibrium points and limit cycles, how to determine, or at least, estimate their domains of attraction (DOA) [2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17]. As will be discussed, in Section 3, the estimation of DOA can be formulated as a constrained nonlinear optimization problem.…”

Numerical algorithm for constructing Lyapunov functions of polynomial differential system

“…These methods include Lyapunov function method [7,[10][11][12][13][14][18][19][20][21][22] and nonLaypunov function method [2-6, 8, 9, 15, 16]. J.R. Hewit and C. Storey [14] have proposed an algorithm to calculate the coefficients of polynomial Lyapunov function.…”

“…[19,20] computer generated Lyapunov function to estimate the stability region of interconnected systems. A. Vannelli and M. Vidyasagar [21] calculate the maximal Lyapunov functions to estimate the domains of attraction for autonomous nonlinear systems. R. Genesio, M. Tartaglia, and A. Vicino [10][11][12], P.P.…”