2010/10/22 by Serdar Yüksel, Sean Meyn, Yüksel, Serdar +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #60J05 #93E03 #94A15 #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Information Theory (cs.IT) #Optimization and Control (math.OC) #Petri Nets in System Modeling #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1010.4820
openalex publication_date 2010/10/22 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly\nsimplified verification theorems for stability for large classes of Markov\nchain models. This is one component of the "fluid model" approach to stability\nof stochastic networks. In this paper we extend the general theory to\nrandomized multi-step Lyapunov theory to obtain criteria for stability and\nsteady-state performance bounds, such as finite moments.\n These results are applied to a remote stabilization problem, in which a\ncontroller receives measurements from an erasure channel with limited capacity.\nBased on the general results in the paper it is shown that stability of the\nclosed loop system is assured provided that the channel capacity is greater\nthan the logarithm of the unstable eigenvalue, plus an additional correction\nterm. The existence of a finite second moment in steady-state is established\nunder additional conditions.\n