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. https://doi.org/10.1155/S1024123X9500007X
A unified approach to fixed-order controller design via linear matrix inequalities
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,-stabilization as a robust stabilization problem, and robust 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 for the unknown matrix . 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 such that and where and are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.
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