Sufficient Conditions for Closed-Loop Control Over Multiple-Access and Broadcast Channels

The problem of closed-loop stabilization of two scalar linear time invariant systems over noisy multiple-access and broadcast communication channels with arbitrarily distributed initial states is addressed. We propose to use communication and control schemes based on the coding schemes introduced by Ozarow et al. for the multiple-access and the broadcast channels with noiseless feedback which are extensions of the Schalkwijk-Kailath coding scheme. By employing the proposed communication and control schemes over the multiple-access and the broadcast channels, we derive stability regions those are sufficient for mean square stability of the two linearly controlled LTI systems.