OPTIMAL ON-LINE OBSERVATION OF ONE TYPE OF TIME-DELAY SYSTEMS

A linear optimal observation problem for one type of time-delay systems with unknown but bounded initial state is under consideration. A fast version of the dual method of linear programming is developed to compute current estimates of it's states. Principal part of this algorithm is a quasireduction of the fundamental matrix of the system. It is shown that to fulfil an iteration, it is sufficient to integrate an auxiliary ordinary system over not large intervals of time. An algorithm of online calculation of current estimates of system's states is also described. The results are illustrated by the example.