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

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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.

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Authors and Affiliations

  1. School of Engineering and Mathematical Sciences, Control Engineering Research Centre, City University, Northampton Square, London, EC1V 0HB, UK

    J. Kiskiras & G. D. Halikias

  2. Department of Electrical and Electronic Engineering, Control and Power Group, Imperial College, London, SW7 2AZ, UK

    I. M. Jaimoukha

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  1. J. Kiskiras
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  2. I. M. Jaimoukha
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  3. G. D. Halikias
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Correspondence to G. D. Halikias.

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Kiskiras, J., Jaimoukha, I.M. & Halikias, G.D. An explicit state-space solution to the one-block super-optimal distance problem. Math. Control Signals Syst. 25, 167–196 (2013). https://doi.org/10.1007/s00498-012-0097-8

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