Mathematical Problems in Engineering

Mathematical Problems in Engineering / 1995 / Article

Open Access

Volume 1 |Article ID 309371 |

T. Iwasaki, R. E. Skelton, "A unified approach to fixed-order controller design via linear matrix inequalities", Mathematical Problems in Engineering, vol. 1, Article ID 309371, 17 pages, 1995.

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

Received25 Apr 1994


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 BGC+(BGC)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 X𝒞1 and X1𝒞2 where 𝒞1 and 𝒞2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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