A Positive Real Lemma Type-Result with Respect to the Anisotropic Norm for Stochastic Systems with Multiplicative Noise. Issue 25 (2018) - Stoica, Adrian–Mihail; Yaesh, Isaac
Abstract: The passivity of discrete–time linear stochastic systems with multiplicative noise is considered, where the systems inputs have bounded anisotropy. Using first principles analysis applying completing the square arguments, it is proved that such systems are passive if a specific Riccati equation has a stabilizing positive semidefinite solution satisfying two additional conditions. The theoretical results are illustrated by a simple numerical example.