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

Mohsen Vatani 1 Morten Hovd 1 Sorin Olaru 2
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : In this paper, controller design for discrete time bilinear systems is investigated by using Sum of Squares (SOS) programming methods and quadratic Lyapunov functions. The class of rational polynomial controllers are 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 SOS 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.
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Mohsen Vatani, Morten Hovd, Sorin Olaru. Control design for discrete-time bilinear systems using the scalarized Schur complement. International Journal of Robust and Nonlinear Control, Wiley, 2017, 27 (18), pp.4492 - 4506. ⟨10.1002/rnc.3807⟩. ⟨hal-01719796⟩

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