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Robust stabilisation of multivariable systems: A super-optimisation approach

Kiskiras, J. (2007). Robust stabilisation of multivariable systems: A super-optimisation approach. (Unpublished Doctoral thesis, City, University of London)


The work aims to derive extended robust stability results for the case of unstructured uncertainty models of multivariable systems. More specifically, throughout the thesis, additive and coprime unstructured perturbation models are considered. Refined robust stabilisation problems of MIMO systems are defined and maximally robust controllers are synthesised in a state-space form.

Unstructured perturbations which destabilise the feedback system for every optimal (maximally robust) controller are identified on the boundary of the optimal ball, i.e. the set of all admissible perturbations with norm equal to the maximum robust stability radius. Boundary perturbations are termed "uniformly destabilising" if they destabilise the closed-loop system for every optimal controller and it is shown that they all share a common characteristic, i.e. a projection of magnitude equal to the maximal robust stability radius, along a fixed direction defined by a pair of maximising vectors (scaled Schmidt pair) of a Hankel operator related to the problem. By imposing a directionality constraint it is shown that it is possible to increase the robust stability radius in every other direction by a subset of all optimal controllers.

In order to solve this problem, super-optimisation techniques are developed. Independently a natural extension of Hankel norm approximations, the so-called super­ optimisation problem is posed and solved explicitly for the case of one-block problems in a state-space setting. It is thus shown that a subset of all maximally robust controllers, namely the class of super-optimal controllers, stabilises all perturbed plants within an extended stability radius 11,*(b), subject to a directionality constraint.

In addition, the work is related to robust stabilisation subject to structured perturbations. The notions of structured robust stabilisation problem, and structured set approximation are defined in connection with the maximised set of permissible perturbations. It is further shown that µ*(J) can serve as an upper bound the structured robust stabilisation problem.

The effect of µ*(J) as an upper bound depends on the compatibility between the two structures, the true structure and the artificial structure of the extended permissible set.

[Look inside the thesis' abstract for an exact version of formulas and equations]

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Engineering
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
[thumbnail of Kiskiras thesis 2007 PDF-A.pdf]
Text - Accepted Version
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