GEOMETRIC STATE-SPACE THEORY IN LINEAR-MULTIVARIABLE CONTROL - STATUS-REPORT

With the renewed emphasis in control theory on qualitative structural issues, as distinct from techniques of optimization, the last decade has brought significant growth in the application of geometric ideas to the formulation and solution of problems of controller synthesis. In this article we review the status of geometric state space theory as developed for application to systems that are linear, multivariable and time-invariant. After a brief summary of the underlying geometric concepts ((A, B)-invariant subspaces and (A, B)-controllability subspaces) we outline two standard problems of feedback control that have been successfully attacked from this point of view, and briefly survey recent results in a range of other topic areas. Then we discuss certain issues of methodology, and conclude with some remarks on computational procedures. © 1979.