Empirical Computation of Reachability Gramian for Linear-Time Varying Systems

This paper deals with the approximate computation of the reachability gramian for linear time-varying(LTV) systems over a finite time interval. To this end, we use state trajectory information obtained by simulating the system for various inputs and initial conditions. We propose three techniques for computing the reachability gramian. The first two techniques use state variable data of the original LTV system realization while the third uses state variable data of the modified adjoint of the original LTV realization. We demonstrate the workability of these methods with the help of a numerical example. Similar to our work, Perev (2018); Perev (2019) deal with computing finite interval gramians of linear time-varying systems using system trajectory information. However, our methods avoid the computation of the state-transition matrix, which is essential in Perev’s work.