On exponentially almost sure stability of random jump systems

This paper is concerned with a class of random
jump systems represented by transition operators, which includes
switched linear systems with strictly stationary switching signals
in infinite modes space as its special case. A series of necessary and
sufficient conditions are established for almost sure stability of
this class of random jump systems under different scenarios. The
stability criteria obtained are further extended to Markov jump
linear systems with infinite states, and hence a unified approach to
describing the almost sure stability of MJLSs is addressed under
this context. All the results in the work are developed for both the
continuous- and discrete-time systems.