An explicit state-space solution to the one-block super-optimal distance problem

Kiskiras, J., Jaimoukha, I. M. & Halikias, G. (2013). An explicit state-space solution to the one-block super-optimal distance problem. Mathematics of Control, Signals, and Systems, 25(2), pp. 167-196. doi: 10.1007/s00498-012-0097-8

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Abstract

An explicit state-space approach is presented for solving the super-optimal Nehari-extension problem. The approach is based on the all-pass dilation technique developed in (Jaimoukha and Limebeer in SIAM J Control Optim 31(5):1115–1134, 1993) which offers considerable advantages compared to traditional methods relying on a diagonalisation procedure via a Schmidt pair of the Hankel operator associated with the problem. As a result, all derivations presented in this work rely only on simple linear-algebraic arguments. Further, when the simple structure of the one-block problem is taken into account, this approach leads to a detailed and complete state-space analysis which clearly illustrates the structure of the optimal solution and allows for the removal of all technical assumptions (minimality, multiplicity of largest Hankel singular value, positive-definiteness of the solutions of certain Riccati equations) made in previous work (Halikias et al. in SIAM J Control Optim 31(4):960–982, 1993; Limebeer et al. in Int J Control 50(6):2431–2466, 1989). The advantages of the approach are illustrated with a numerical example. Finally, the paper presents a short survey of super-optimization, the various techniques developed for its solution and some of its applications in the area of modern robust control.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00498-012-0097-8
Uncontrolled Keywords: Super-optimal Nehari-extension problems, Hankel operator, All-pass dilations, H∞-optimal control, Maximally robust stabilization
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/14862

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