Finite-Time Stabilization of Switching Markov Jump Systems with Uncertain Transition Rates

Finite-time behavior of switching networks

“…In addition to necessary and sufficient τ -SS conditions, connections between τ -MSS and τ -EMSS (mean square τ -stable and exponentially mean square τ -stable, respectively) were also studied [12]. Recently, [14] used Lyapunov arguments to provide sufficient FTS conditions for the case where Markov chains are unknown. Systems that exhibit linear dynamics in each discrete mode, and Markovian transitions between modes are also known as Markov Jump Linear Systems or MJLS; the stability of MJLS has been a topic of recent research [15], [16].…”

“…Remark 4: Theorems 1 to 3 show network topologies have a clear impact on system stability because, along with the Markov chain, they determine linear operators (10), (11), and (14). There is a much broader class of systems (including non-networked ones) for which our results are valid, but we explicitly adopted this general setting because the realworld networks we are interested in do not adhere to special topologies, such as ring or star, as empirical evidence shows [17].…”

Passivity and passification for switching Markovian jump systems with time‐varying delay and generally uncertain transition rates

“…Remark 13 In practice, due to the restriction of measurement conditions, when the system works in the th subsystem, if the transition rate from mode at time to mode at time is not measured, then the unknown element can be described by ‘ ’. In simulation, according to the chosen method of [14, 19, 25, 42–44], the generally uncertain transition rate matrices in the form of (43) are chosen stochastically which meet the requirements. Remark 14 Compared with the existing papers in [44, 45], using the fixed connection weighting matrices, we cannot get . Therefore, to some extent, using the free connection weighting matrices can reduce some conservativeness. Remark 15 Compared with the existing work in [22–25], the time delay is not considered, which shows that our results are new. Remark 16 If Lyapunov function is chosen in the form of (38), we cannot get , which means that Lyapunov function (14) may reduce some conservativeness. Remark 17 If the transition rate matrices are uncertain bounded as follows: …”

“…The exponential – controller for discrete‐time switching Markov jump linear systems was designed in [24]. The problem of finite‐time state feedback controller for SMJS with uncertain transition rates was addressed in [25]. Sufficient conditions for finite‐time stability of discrete‐time switching dynamics Markovian jump linear systems with time‐varying delay were proposed and the state feedback controller was constructed in [26].…”

Robust finite–time stochastic stabilization and fault–tolerant control for uncertain networked control systems considering random delays and probabilistic actuator faults

“…During the past few years, researchers have stressed on the finite–time stability, which regards the state trajectories boundedness over a finite time interval. As a result, a series of studies on finite–time stochastic stability (FTSS) or finite–time stochastic boundedness (FTSB) of MJSs have been presented (Bahreini and Zarei, 2018; Luan et al, 2015; Shen et al, 2016; Zuo et al, 2012a,b). Although it is of great significance to develop the finite–time FTC for Markov–driven NCSs with complex TPs, there is still no solid result available in this area, which motivates this study.…”