TY - JOUR N2 - The stability and positivity of linear positive Markovian jump systems with respect to part of the variables is considered. The methodologies of stability of positive systems with known transition probabilities based on common linear copositive Lyapunov function and stability of linear systems with respect to part of the variables are combined to find sufficient conditions of the stochastic stability and positivity of Markovian jump systems with respect to part of the variables. The results are extended for a class of nonlinear positive Markovian jump systems with respect to part of the variables. An example is given to illustrate the obtained results. L1 - http://www.journals.pan.pl/Content/113670/PDF/10_769-776_01081_Bpast.No.67-4_13.09.19_K1_TeX.pdf L2 - http://www.journals.pan.pl/Content/113670 PY - 2019 IS - No. 4 EP - 775 DO - 10.24425/bpasts.2019.130186 KW - hybrid system KW - Lyapunov method KW - Markov jump system KW - stability and positivity with respect to the part of variables A1 - Socha, L. VL - 67 DA - 31.08.2019 T1 - Stability and positivity with respect to part of the variables for positive Markovian jump systems SP - 769 UR - http://www.journals.pan.pl/dlibra/publication/edition/113670 T2 - Bulletin of the Polish Academy of Sciences Technical Sciences ER -