Mean square detectability of multi-output networked systems over finite-state fading channels

This paper studies the mean square quadratic (MSQ) detectability for multi-output networked systems over finite-state fading channels. The unreliability from the plant output to the estimator input is described by multiplicative noises. A finite-state random process is introduced to model time-varying fading channels. Necessary and sufficient conditions for MSQ detectability are given in the form of algebraic Riccati equations or linear matrix inequalities. In addition, explicit conditions on network for MSQ detectability over finite-state independent identically distributed (i.i.d.) fading channels are presented in terms of the Mahler measure of the unstable and multi-output plant. Finally, application to Gilbert-Elliott channels (GECs) is provided to demonstrate the derived results.