Neutral-type Delay Research Articles

Canonical delays, Rn(s)-controllability and function space controllability of linear differential-difference systems

A linear control system with delays of neutral type is characterized by a pair of matrices over the ring R0(s) of proper rational functions which can be embedded into the field IR(s) of rational functions. This leads to a natural concept of IRn (s)-controllability and to canonical forms related to those known for matrices over reals as Luenberger and Brunovsky canonical forms. Algebraic criteria for Rn (s)-controllability are derived. The dynamical properties of transformations leading to canonical forms are examined. In the case of Brunovsky-type canonical form the transformed system is an interconnection of a purely discrete-time (difference) system containing a minimal number of delay elements (canonical delays) and ordinary differential systems (without delays). It is shown that Rn(s)-controllability can be characterized equivalently as the property that the closure (in Lp) of the attainable subspace of final states at time t≥nh has finite co-dimension (n = number of system equations, h== delay).