Controllability of Discrete‐time Bilinear Systems With Uncertainties

ABSTRACT Uncertainties often arise in system modeling, rendering traditional controllability analysis methods ineffective. However, establishing algebraically verifiable controllability criteria for nonlinear systems is an extremely difficult task. As a consequence, robust controllability remains unexplored for most nonlinear systems. In this article, we study controllability of discrete‐time bilinear systems with uncertainties. By using the notion of near‐controllability, we establish, for the first time, algebraic robust controllability criteria for both homogeneous and inhomogeneous uncertain bilinear systems, allowing the systems to be robustly controllable under uncertainties. Furthermore, we also provide practical algorithms to verify robust controllability of the uncertain bilinear systems. The proposed criteria and algorithms work for the systems in any finite dimension and are easy to implement. These results not only enrich the robust controllability theory of discrete‐time bilinear systems but also open new avenues for analyzing how parametric uncertainties affect the controllability of discrete‐time bilinear systems and bilinear networks. Examples are given to illustrate the presented algebraic robust controllability criteria.