Verified stability analysis of continuous-time control systems with bounded parameter uncertainties and stochastic disturbances
For nonlinear systems, feedback control strategies have to be parameterized in such a way that they guarantee asymptotic stability in a certain neighborhood of desired operating points or desired trajectories. Due to not exactly known initial conditions, parameter uncertainties, and measurement errors characterizing dynamic system models in real applications, interval techniques are taken into consideration in this paper to verify stability properties of nonlinear uncertain systems with continuous-time dynamics. These techniques aim at a computation of guaranteed regions of attraction for asymptotically stable equilibria. The practical applicability is shown for the analysis of tracking controllers for ship motions in an uncertain environment. In this application, we focus on analyzing the effects of parameter uncertainties on the domains in the state-space that can be proven to belong to the region of attraction of the desired equilibrium.
stability analysis guaranteed regions of attraction interval uncertainties control of uncertain dynamical systems lyapunov functions