Control Design and Analysis for Discrete Time Bilinear Systems using Sum of Squares Methods
Journal article, Peer reviewed
Permanent lenke
http://hdl.handle.net/11250/284408Utgivelsesdato
2014Metadata
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Originalversjon
IEEE Proceedings : Conference on Decision and Control (CDC) 2014 10.1109/CDC.2014.7039874Sammendrag
In this paper, stabilization of discrete time bilinear systems is investigated by using Sum of Squares (SOS)
programming methods and a quadratic Lyapunov function.
Starting from the fact that global asymptotic stability cannot
be proven with a quadratic Lyapunov function if the controller
is polynomial in the states, the controller is instead proposed
to be a ratio of two polynomials of the states. First, a simple
one-step optimal controller is designed, and it is found that
it is indeed defined as a ratio of two polynomials. However,
this simple controller design does not result in any stability
guarantees. For stability investigation, 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 convergence of the bilinear system. Input constraints
can also be accounted for in the optimization problem.