Necessary and sufficient asymptotic stability criterion for 2-D positive systems with time-varying state delays described by Roesser model

This study addresses the stability problem of two-dimensional (2-D) positive systems described by Roesser model and involving delays in the states. The delays are time varying and bounded. A necessary and sufficient stability condition is established for such systems. It is shown that a 2-D positive system with time-varying delays is asymptotically stable for any bounded delays if and only if the corresponding constantly delayed system is asymptotically stable, or equivalently, if and only if the sum of the system matrices is a Schur matrix. An example illustrates the theoretical result.