Beschreibung:
The stability of equilibrium points plays a fundamental role in dynamical systems. For nonlinear dynamical systems, which represent the majority of real plants, an investigation of stability requires the characterization of the domain of attraction (DA) of an equilibrium point, i.e., the set of initial conditions from which the trajectory of the system converges to such a point. It is well-known that estimating the DA, or even more attempting to control it, are very difficult problems because of the complex relationship of this set with the model of the system.
SOS Polynomials.- Optimization with SOS Polynomials.- Preliminaries of Nonlinear Systems.- Domain of Attraction in Polynomial Systems.- Domain of Attraction in Uncertain Polynomial Systems.- Domain of Attraction in Non-polynomial Systems.- Domain of Attraction via Multiple Lyapunov Function.- Miscellaneous.