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Computing the controllability radius: a semi-definite programming approach

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3 Author(s)
B. Dumitrescu ; Department of Automatic Control and Computers, `Politehnica¿ University of Bucharest, Spl. Independent¿ei 313, 060042 Bucharest, Romania Tampere International Center for Signal Processing, Tampere University of Technology, Tampere, Finland E-mail: bogdan@schur.pub.ro ; B. C. Sicleru ; R. Stefan

A semi-definite programming (SDP) approach to compute the controllability radius is proposed in this paper. The initial nonconvex optimisation problem is transformed into the minimisation of the smallest eigenvalue of a bivariate real or trigonometric polynomial with matrix coefficients. A sum-of-squares relaxation leads to the SDP formulation. A similar technique is used for the computation of the stabilisability radius. The approach is extended to the computation of the worst-case controllability radius for systems that depend polynomially on a small number of parameters. Experimental results show that the proposed methods compete well with previous ones in a complexity/accuracy trade-off.

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IET Control Theory & Applications  (Volume:3 ,  Issue: 6 )