Lyapunov Criterion for Stochastic Systems and Its Applications in Distributed Computation

Qin, Y., Cao, M. & Anderson, B. D. O., Feb-2020, In : IEEE-Transactions on Automatic Control. 65, 2, p. 546-560 15 p., 8691522.

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This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system’s solutions after a finite number of steps, but without necessarily
strict decrease at every step, in contrast to the classical stochastic Lyapunov theory. As the first application of this new Lyapunov criterion, we look at the product of any random sequence of stochastic matrices, including those with zero diagonal entries, and obtain sufficient conditions to ensure the product almost surely converges to a matrix with identical rows; we also show that the rate of convergence can be exponential under additional conditions. As the second application, we study a distributed network algorithm for solving linear algebraic equations. We relax existing conditions on the network structures, while still guaranteeing the equations are solved asymptotically.
Original languageEnglish
Article number8691522
Pages (from-to)546-560
Number of pages15
JournalIEEE-Transactions on Automatic Control
Issue number2
Early online date15-Apr-2019
Publication statusPublished - Feb-2020

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