Stability of Markovian Jump Linear Systems over Networks with Random Delays

Almost sure stability for a class of dual switching linear discrete‐time systems

“…On the other hand, the sufficient condition of mean square stabilization, for the discrete‐time switching Markov jump linear systems, was described by Qu et al 22 The transition probability of the Markov chain is variable and is determined by the current position of deterministic switching 23 . Moreover, some new applications of the research results, on dual switching systems, are discussed in other works 24–27 …”

“…23 Moreover, some new applications of the research results, on dual switching systems, are discussed in other works. [24][25][26][27] Different from the aforementioned statements and as described in the abstract, we concentrate on the exponentially almost sure stability problem for dual switching discrete-time linear systems with exponential uncertainty. First, by using the Taylor series approximation and convex polynomial technique, the variable dual switching discrete-time linear system, with exponential uncertainty, is expressed as a variable dual switching discrete-time linear polytopic system with an additive norm-bounded uncertainty.…”

Mean square stabilization of discrete‐time switching Markov jump linear systems

“…Markov jump linear system (MJLS) is a class of stochastic switched systems with wide applications. They are often used to model the dynamics of systems with random faults, unpredictable events, structural changes, networked control systems, etc . In recent decades, a great deal of attention has been devoted toward the stability of stochastic systems, particular in the case that transition probabilities is unknown or uncertain .…”

“…They are often used to model the dynamics of systems with random faults, unpredictable events, structural changes, networked control systems, etc. [1][2][3][4][5][6][7] In recent decades, a great deal of attention has been devoted toward the stability of stochastic systems, particular in the case that transition probabilities is unknown or uncertain. 8,9 Several different notions of stability are defined, respectively, for stochastic systems, which are also applicable to MJLSs.…”

Stochastic Stabilization of Itô Stochastic Systems with Markov Jumping and Linear Fractional Uncertainty

“…Modeled by a set of linear systems with the transitions among the linear systems governed by the Markov chain, the Markov jumping linear system (MJLS) can characterize and model different types of systems [1], for instance, fault-tolerant systems, target tracking systems, manufactory processes, networked control systems, multiagent systems, and so on. In the past years, many important results on MJLS have been addressed in the literature, such as, the stability analysis and control design which were discussed in [2][3][4][5][6][7][8]. Besides the aforementioned theoretical studies, MJLS also found applications in practical systems, such as networked direct current motor systems [9].…”