A unified approach to fixed-order controller design via linear matrix inequalities

T. Iwasaki and R. E. Skelton

Mathematical Problems in Engineering, 1995, vol. 1, 1-17

Abstract:

We consider the design of fixed-order (or low-order) linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem, 𝒬 -stabilization as a robust stabilization problem, and robust L ∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI) of the type B G C + ( B G C ) T + Q < 0 for the unknown matrix G . Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured) positive definite matrix X such that X ∈ 𝒞 1 and X − 1 ∈ 𝒞 2 where 𝒞 1 and 𝒞 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:309371

DOI: 10.1155/S1024123X9500007X

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