Control design for discrete-time bilinear systems using the scalarized Schur complement

In this paper, controller design for discrete-time bilinear systems is investigated by using sum of squares programming methods and quadratic Lyapunov functions. The class of rational polynomial controllers is considered, and necessary conditions on the degree of controller polynomials for quadratic stability are derived. Next, a scalarized version of the Schur complement is proposed. For controller design, the Lyapunov difference inequality is converted to a sum of squares problem, and an optimization problem is proposed to design a controller, which maximizes the region of quadratic stability of the bilinear system. Input constraints can also be accounted for. This is the peer reviewed version of the following article: [Control design for discrete-time bilinear systems using the scalarized Schur complement], which has been published in final form at [http://onlinelibrary.wiley.com/doi/10.1002/rnc.3807/abstract]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Locked until 28.3.2018 due to copyright restrictions.