Finite-time stochastic contractive boundedness of Markovian jump systems subject to input constraints

•FTSCS and FTSCB are introduced.•The newly stochastic Lyapunov-Krasovskii functional and novel activation function conditions are proposed.•A relaxation scheme for incomplete transition probability descriptions is introduced.

This paper studies the finite-time stochastic contractive boundedness problem for a class of Markovian jump linear systems subject to input constraints. First of all, by employing exogenous disturbance, two novel concepts, namely finite-time stochastic contractive stability (FTSCS) and finite-time stochastic contractive boundedness (FTSCB) are introduced. Secondly, a relaxation scheme for incomplete (i.e., partly known, unknown, and uncertain) transition probability descriptions is introduced. Then, two kinds of design methodology of observer-based controllers are proposed. All the design conditions are established by employing a set of linear matrix inequalities (LMIs). At last, numerical examples are given to demonstrate the effectiveness of the proposed approach.