On parametric stabilization of uncertain singularly perturbed systems
A linear uncertain singularly perturbed system whose trivial solution is unstable for the values of a parameter from a certain domain, is considered. The problem is to parametrically stabilize the original system, i.e. to choose a control that guarantees the absolute stability of a moving equilibrium state of the obtained nonlinear uncertain singularly perturbed system for all values of the parameter from a certain domain and to determine this domain. The obtained nonlinear singularly perturbed system allows one to choose a degenerate subsystem and a boundary layer. However, they do not enable one to construct the components of a Lyapunov vector function and to verify the stability of the original system because of the absence of information on the stability of these subsystems. That is why, in this paper, a matrix-valued Lyapunov function is used for the investigation of the absolute parametric stability of uncertain singularly perturbed systems.
scientific article; zbMATH DE number 6192522