A computational method for determining quadratic lyapunov functions for non-linear systems
Automatica (Journal of IFAC)
Journal of Approximation Theory
Brief paper: Local stability analysis using simulations and sum-of-squares programming
Automatica (Journal of IFAC)
Brief paper: Lyapunov-based stability analysis automated by genetic programming
Automatica (Journal of IFAC)
Brief paper: Estimating the domain of attraction for non-polynomial systems via LMI optimizations
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Nonlinear dynamic systems design based on the optimization of the domain of attraction
Mathematical and Computer Modelling: An International Journal
Estimation of domains of attraction: A global optimization approach
Mathematical and Computer Modelling: An International Journal
Rational Lyapunov functions for estimating and controlling the robust domain of attraction
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Hi-index | 22.16 |
In this paper we present various theoretical and computational methods for estimating the domain of attraction of an autonomous nonlinear system. These methods are based on the concept of a maximal Lyapunov function, which is introduced in this paper. A partial differential equation characterizing a maximal Lyapunov function is derived, and the relationships of this equation as compared to Zubov's partial differential equation are discussed. An iterative procedure is given for solving the new partial differential equation. This procedure yields Lyapunov function candidates that are rational functions rather than polynomials. The method is applied to four two-dimensional examples and one three-dimensional example, and it is shown that the estimates obtained using this method are, in many cases, substantially better than those obtained using known methods.