Positive observer design for positive Markovian jump systems with mode-dependent time-varying delays and incomplete transition rates

The paper is concerned with positive observer design for positive Markovian jump systems with incomplete transition rates and time delays that are mode-dependent and time-varying. Firstly, by applying an appropriate co-positive type Lyapunov-Krasovskii function and free-connection weighting vectors, sufficient conditions are proposed to ensure stochastic stability of the error positive system and existence of the positive observer. All the proposed conditions are derived in linear programming. Finally, an example is given to demonstrate the validity of the main results.