DETECTABILITY OF LINEAR DISCRETE TIME LINEAR SYSTEMS DEFINED BY POSITIVE OPERATORS

In this paper we extend the notion of detectability, introduced in [1] in connection with stochastic systems, to a more general class of linear discrete time systems defined by positive operators. We also extend a result in [1], which mainly state that, under detectability hypothesis, the considered linear discrete-time system is exponentially stable if and only if an associated Lyapunov equation has a bounded solution.