A unified approach to fixedorder controller design via linear matrix inequalities
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We consider the design of fixedorder (or loworder) linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem, 2stabilization 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 fixedorder controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixedorder 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. © 1995, OPA (Overseas Publishers Association).
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Iwasaki, T., & Skelton, R. E.
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