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.

JO - Bulletin of the Polish Academy of Sciences: Technical Sciences L1 - http://sp.czasopisma.pan.pl/Content/113670/PDF/10_769-776_01081_Bpast.No.67-4_13.09.19_K1_TeX.pdf L2 - http://sp.czasopisma.pan.pl/Content/113670 IS - No. 4 EP - 775 KW - hybrid system KW - Lyapunov method KW - Markov jump system KW - stability and positivity with respect to the part of variables ER - A1 - Socha, L. VL - 67 JF - Bulletin of the Polish Academy of Sciences: Technical Sciences SP - 769 T1 - Stability and positivity with respect to part of the variables for positive Markovian jump systems UR - http://sp.czasopisma.pan.pl/dlibra/docmetadata?id=113670 DOI - 10.24425/bpasts.2019.130186