Stabilization of Large-scale Bilinear Systems via the ε-Coupling Approach

Abstract

The stabilization problem of a class of ε-coupled large-scale bilinear systems via state-variable feedback is studied. Using Lyapunov theory the stabilizing control is shown to be of the quadratic-state-feedback type. The basic result of the paper is that the stabilizing controller of the overall ε-coupled bilinear system can be implemented as a linear combination of the stabilizing controllers of the two decoupled subsystems to which the system reduces when ε=0, and an ε-dependent term which is due to the ε-coupling that actually exists between them when ε≠0. The results are first given for strictly bilinear systems, and are then extended to bilinear systems of complete form. Both the single-parameter and multiparameter coupling cases are considered for scalar as well as vectorial controls. Three nontrivial examples illustrate the applicability of the theory.