21 December 2011, h.10:30 - Aula 326 DEI-A
Stabilization over Markov Feedback Channels
University of California at San Diego, San Diego, CA, USA
This work deals with the problem of mean-square stabilization of a discrete-time linear dynamical system over a time-varying digital feedback channel. In particular, the channel rate evolves according to an arbitrary time invariant, positive recurrent Markov chain with a finite number of states. In the scalar case, it is shown that the system can be stabilized if and only if a Markov jump linear system describing the evolution of the estimation error at the decoder is stable, that is, if and only if the product of the unstable mode of the system and the spectral radius of a second moment matrix that depends only on the Markov feedback rate is less than one. This result generalizes several previous data rate theorems that appeared in the literature, quantifying the amount of instability that can be tolerated when the estimated state is received by the controller over a noise free digital channel. In the vector case, a necessary condition for stabilization is derived and a corresponding control scheme is presented, which is tight in some special cases and which strictly improves on a previous result on stability over Markov erasure channels.
Lorenzo Coviello is a PhD student in Electrical and Computer Engineering at the University of California San Diego. His advisor is Prof. Massimo Franceschetti. Lorenzo's research interests span from network science and social networks (principally, the mathematical and algorithmic modeling of human behavior) to the theory of communication and control systems (in particular, the control of dynamical systems under communication constraints). At UCSD, Lorenzo coordinates the CWC Communication and Networking Seminar Series. Before joining UCSD, Lorenzo obtained a Laurea Specialistica in Telecommunication Engineering from the University of Padova.