FEEDBACK STABILIZATION OF LINEAR-SYSTEMS WITH DISTRIBUTED DELAYS IN STATE AND CONTROL VARIABLES

Solving a generalized characteristic matrix equation (GCME) of a linea r retarded system is the crux for stabilizing the system using reducti on technique. This note gives the solution of GCME under the general c ondition that the eigenvalues occur in the spectrum of the system with algebraic and geometric multiplicities being greater than or equal to one. The main idea is to transform the GCME into a group of linear al gebraic equations. A sufficient condition for the existence of the sol ution to the linear algebraic equations is established. A key lemma fo r stabilizing the systems under the above general condition is also pr oved.