Stochastic stability and robust stabilization of semi‐Markov jump linear systems

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Robust stabilisation for non-linear time-delay semi-Markovian jump systems via sliding mode control (2017, background): “Lemma 1 [17]: Let T, M, N, and F be matrices with appropriate dimensions with FTF ≤ I, then for any positive scalar ε > 0, there holds”
Reliable mixed passive and ℋ∞ filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures (2015, methodology): “In the context of SMJLSs, the stability analysis problem was solved in [28, 29], some available controller design methods were proposed in [30], and the H1 control problem was discussed in [31].”
Event-triggered dissipative filtering for networked semi-Markov jump systems and its applications in a mass-spring system model (2016, unknown): “In practice, the transition rate πi j ( ) of semiMarkov process can be partly available [7].”
A survey on Markovian jump systems: Modeling and design (2015, background): “However, the main proposition in [117] to partition the sojourntime into M sections in each working mode is relatively conservative and practically infeasible.”
Stability and Stabilization of Discrete-Time Semi-Markov Jump Linear Systems via Semi-Markov Kernel Approach (2016, background): “On the other hand, the developed theories on semi-Markov jump linear systems (S-MJLSs) are far away from maturity yet, although the systems have been investigated since 1960s, see for example, [8], [9], [13] and [14].”