H_∞ structured model reduction algorithms for linear discrete systems via LMI-based optimisation

Abstract

In this article, H _∞ structured model reduction is addressed for linear discrete systems. Two important classes of systems are considered for structured model reduction, i.e. Markov jump systems and uncertain systems. The problem we deal with is the development of algorithms with the flexibility to allow any structure in the reduced-order system design, such as the structure of an original system, decentralisation of a networked system, pole assignment of the reduced system, etc. The algorithms are derived such that an associated model reduction error guarantees to satisfy a prescribed H _∞ norm-bound constraint. A new condition for the existence of desired reduced-order models preserving a certain structure is presented in a set of linear matrix inequalities (LMI) and non-convex equality constraints. Effective computational algorithms involving LMI are suggested to solve the matrix inequalities characterising a solution of the structured model reduction problem. Numerical examples demonstrate the advantages of the proposed model reduction method.

Keywords:

• H _∞ design
• structured model reduction
• Markovian jump linear systems
• uncertain systems
• bilinear matrix inequality
• linear matrix inequality

Acknowledgement

The research is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).