Application of discrete/continuous signal-theory to discrete-time state-estimation problems for linear dynamical systems with intersample variations of inputs

This paper, a continuation of a discrete/continuous signal-theory presentation (for original paper see C.D. Johnson, ibid., (2003)), describes the application of discrete/continuous (D/C) signal ideas to the problem of discrete-time state-estimation for linear dynamical systems with intersample variations of system inputs. It is shown that the more general D/C signal representation of nonconstant system inputs leads to a new, generalized form of state-estimation algorithm (state-observer; Kalman filter) that can produce improved state-estimation performance compared to traditional discrete-time state-estimation algorithms which use zoh-type representations of system inputs. The results are generalized to include cases of non-periodic [event-driven] sampling.