Event-Triggered Second Moment Stabilization under Markov Packet Drops

Event‐triggered second‐moment stabilisation under action‐dependent Markov packet drops

“…in the i.i.d. case [21] and in the Markov channel case in [24]). The reason for doing this is that in case of non-action-dependent channels (P 0 = P 1 ), once S j is known, the resulting closed form of the probability functionΩ D (w, ) is the same irrespective of whether we condition the probability in (23)…”

“…The value of B * defined in Proposition 4.2 can be numerically computed using the procedure in the Appendix, which is based on the proof of Lemma IV.13 in [21]. We now provide a closedform expression of the performance-evaluation function  D ) with its closed form from (21) and that ofΩ D (w, S j ) from (24). Correspondingly, we get an expression that is the sum of multiple infinite series, as in the derivation of  D k in Lemma 4.2.…”

“…packet drops. An exception in the works on event-triggered control is our previous paper [24], which considers Markov packet drops. Even in the literature on NCS, a very common assumption is that the packet drops are i.i.d.…”

“…However, [21] consider only i.i.d. Bernoulli packet drops and [24] consider Markov packet drops. In contrast, here we consider action-dependent Markov packet drops, which results in a coupling of the evolution of the plant and channel states.…”

“…We provide a necessary condition on the plant dynamics and the channel parameters for our transmission policy to achieve the control objective. This necessary condition is similar to the conditions often found in the data rate limited control [45] and NCS in general. The proposed event‐triggered transmission policy is similar in spirit to our earlier work [21, 24]. However, [21] consider only i.i.d.…”