A Kalman filter-based stable dynamic inversion for discrete-time, linear, time-varying systems

in this paper the problem of estimating an unknown input for discrete-time, non-minimum phase, multivariable, linear time-varying systems (LTV) is considered. The initial condition of the plant may be unknown and stochastic process and measurement noise are included. The input signal is modelled as a random walk with drifts. Then it is estimated using a Kalman filter for a uniformly detectable augmented system. A necessary and sufficient condition for the detectability of the augmented system is provided. A Kalman filter-based stable dynamic inversion (SDI) for LTV systems is obtained as a consequence of our solution to the proposed problem. The inversion technique can be applied to achieve output tracking for LTV systems in the presence of non-minimum phase zeros and measurement and/or system noise. We are mainly motivated by typical need to replicate time signals in the automobile industry. Similar problems appear also in other fields as machine tool applications, aeronautic industry a.o.