On output static feedback in linear time-invariant finite-dimensional systems.

摘要

The present work is intended to be a contribution to the theory of linear systems. It is mainly devoted to address (and it is motivated by) the problem of output static stabilization for linear time-invariant finite-dimensional systems.; A necessary and sufficient condition for output static stabilization (that is computable in terms of the solvability of a concave programming problem) is presented. By imposing an extra (artificial) constraint to the aforementioned condition, a new (conservative) output static stabilization concept is introduced. The meaning, the implications, the consequences, and the relevance of the introduced new stabilization concept is analyzed and investigated. Among the numerous results presented are included: convex conditions for output static stabilization and parameterization of stabilizing controllers (in the sense of the new concept), and a generalization of the celebrated Lyapunov's theorem.; In another line of work, a novel characterization for output static stabilizing controllers is presented. This characterization is presented in terms of the stability robustness in a closed-loop interconnection with respect to a special class of operations performed on the controller. A new technical tool is introduced which provides with information that is related with the property of a stabilizing controller of being static. The technical results presented are also of independent interest in linear systems theory.