| Popis: |
The dynamics of many mechanical systems can be described, or approximated by smooth vector fields in d-dimensional space Rd. External and internal excitations as well as modeling uncertainties are incorporated in the vector fields as families of (time-varying) functions, possibly with their own dynamics. The problem then is to study the response behavior of the system under the given uncertainty structure. In this paper we analyze the stability of uncertain systems at an equilibrium point, using the concept of stability radii. Roughly, a stability radius is the smallest excitation range such that a (time-varying) perturbation within this range can render the system unstable. Since we consider time-varying perturbations, the precise stability radius of the system is determined by the maximal Lyapunov exponent of the linearization at the equilibrium point. Several examples illustrate the theory and compare the precise stability radius to the one obtained via Lyapunov function techniques. |
