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This paper works on the stochastic stabilization of an interconnected Markovian jump system. The stabilization is implemented by means of a decentralized observer-based output control with sector nonlinearities. The resulting closed-loop system tolerates some failures of control components and/or control saturation, etc. Based on Lyapunov method a sufficient condition of solvability for the problem is presented. An algorithm for designing of the observer-based output feedback controller is given in terms of linear matrix inequalities (LMIs).