On a Detectability Concept of Discrete-Time Infinite Markov Jump Linear Systems

Abstract

This paper introduces a concept of detectability for discrete-time infinite Markov jump linear systems that relates the stochastic convergence of the output with the stochastic convergence of the state. It is shown that the new concept generalizes a known stochastic detectability concept and, in the finite dimension scenario, it is reduced to the weak detectability concept. It is also shown that the detectability concept proposed here retrieves the well-known property of linear deterministic systems that observability is stricter than detectability.

Key Words:

• Detectability
• Infinite Markov state space
• Markov jump systems
• Stochastic systems

Mathematics Subject Classification:

• 93E03
• 93B07
• 60J75

ACKNOWLEDGMENT

Research supported in part by FAPESP, Grant 01/12233-2; CNPq, Grant 300721/86-2; PRONEX, Grant 015/98 “Control of Dynamical Systems, ” and the IM-AGIMB Grant.