Energy-aware control: &#x2113;<inf>2</inf> gain for closed-loop systems implemented with stochastic schedulers

Stability and Disturbance Attenuation for Markov Jump Linear Systems with Time-Varying Transition Probabilities

“…where (3) follows by plugging in the definition of Ỹψ (i, k + 1), interchanging the order of summation, and recognizing an iterated expectation. Definition 7 and equation ( 4) show (2b) with ν > 0 by the hypothesis on M .…”

“…The Markov jump linear system abstraction finds application in many areas including economics [1], fault-tolerant control [2], energy-aware control [3], and networked control [4], [5]. Despite the prevalence of Markov jump linear systems, little attention has been paid to the case when the Markov chain transition probabilities are time-varying, and almost no attention has been paid to the case when the Markov chain transition probabilities are time-varying and a priori unknown.…”

“…11.4.2]) and provide a sufficient condition for uniform stochastic stability subject to a dwell-time constraint. Lutz and Stilwell [3] examine a particular class of time-inhomogeneous Markov jump linear systems with a priori unknown transition probabilities, provide sufficient conditions for uniform mean square stability and uniform stochastic disturbance attenuation, and present a sufficient condition for uniform stochastic stability subject to an average dwell-time constraint.…”