Composite TPs Case
This chapter is concerned with the robust stability problem for a class of discrete-time uncertain Markov jump systems (MJSs) with both partially unknown and uncertain transition probabilities (TPs). Therefore, the scenario is more practical and such TPs comprise three sorts: known, uncertain and unknown. Moreover, the system considered in this chapter is specifically meant to be a class of Markov jump neural networks (MJNNs) with uncertainties and perturbations. The parameters uncertainties are considered to be norm-bounded and the stochastic perturbations are described in forms of the Brownian motion. By invoking the property of the transition probabilities matrix (TPM) and the convexity of uncertain domains, a sufficient stability criterion for the underlying system is derived. Furthermore, a monotonicity is observed in concern of the maximum value of a given scalar which bounds the stochastic perturbation that the system can tolerate as the level of the defectiveness varies.