A unified approach to fixed-order controller design via linear matrix inequalities Academic Article uri icon


  • 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 robustLcontrol 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 typeBGC+(BGC)T+Q<0for the unknown matrixG. 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 matrixXsuch thatX1andX12where1and2are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

published proceedings

  • Mathematical Problems in Engineering

author list (cited authors)

  • Iwasaki, T., & Skelton, R. E.

citation count

  • 8

complete list of authors

  • Iwasaki, T||Skelton, RE

publication date

  • January 1995