Stability analysis for stochastic hybrid systems: A survey

Invariant Sets Analysis for Constrained Switching Systems

“…The relation with the maximal safe set is stated in Corollary 2 which is a consequence of Theorem 3 and the definition of the maximal invariant multi-set. We note that we can deduce even more refined types of invariance, such as, e.g., returnability [32] and recurrence [33].…”

Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise

“…, 0) is also a trivial solution of the stochastic model (1.5) . In this section, stochastic stability [35,36] of the disease-free equilibrium is investigated, including stability in probability and p th moment asymptotic stability. Denote the threshold …”

Stochastic hybrid systems: A modeling and stability theory tutorial

“…For more details, we refer the reader to [5,§IV]. 7 We use S r pKq to denote the set of solutions to (33) with initial conditions belonging to K Ă R n . 6 As such, due to Item 2 above, x can be thought of as a mapping from Ω to the space of (not identically empty) outer semicontinuous set-valued mappings from R 2 to R n .…”

“…The paper [7] contains a recent survey of such results. As indicated there, some of the foundational frameworks for stochastic hybrid systems include piecewise deterministic Markov processes [8], [9], diffusions driven by Lévy processes [10], Markov jump systems [11], hybrid switching diffusions [12], [13], and stochastic hybrid automata [14].…”