Regulation of linear systems with fixed noncommensurate point delays

Abstract

The first solution is given to the open problem of stabilizability and detectability (necessary sufficient conditions for internal stabilization by feedback) of retarded and a large class of linear neutral delay-differential systems with several fixed, noncommensurate point delays, using casual compensators (observers and state-feedback or dynamic output feedback) which are also the same type of neutral or retarded delay differential systems with fixed, point delays only. Our results are rank conditions on the system matrices [zI-F:G] and [zI-FT:HT] evaluated at points in the complex plane and are the weakest possible generally applicable sufficient such rank conditions for stabilization of neutral systems in the light of what is known on the stabilizability of such systems. These conditions are necessary for most practical purposes. The class of systems we consider include all retarded delay-differential systems with noncommensurate, fixed, point delays. In the case of retarded systems, these rank conditions are necessary and sufficient conditions for stabilization via compensators which are causal retarded delay-differential systems with fixed, point delays only.