caa a22 4500 606206116 CHVBK 20210128101010.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00034-015-9981-z doi (NATIONALLICENCE)springer-10.1007/s00034-015-9981-z $$L_1$$ L 1 Control for Positive Markovian Jump Systems with Time-Varying Delays and Partly Known Transition Rates [Elektronische Daten] [Wenhai Qi, Xianwen Gao] This paper deals with the problem of $$L_1$$ L 1 control for positive Markovian jump systems with time-varying delays and partly known transition rates. Firstly, by the use of appropriate co-positive type Lyapunov function, sufficient conditions for stochastic stability of positive Markovian jump systems with time-varying delays and partly known transition rates are proposed. Then, $$L_1$$ L 1 -gain performance of the system considered is analyzed. Based on the results obtained, a state feedback controller is constructed such that the closed-loop Markovian jump system is positive and stochastically stable with $$L_1$$ L 1 -gain performance. All the proposed conditions are derived in linear programming. Finally, an example is given to demonstrate the validity of the main results. Springer Science+Business Media New York, 2015 Positive Markovian jump systems nationallicence Partly known transition rates nationallicence Stochastic stability nationallicence Linear programming nationallicence Qi Wenhai College of Information Science and Engineering, Northeastern University, 110819, Shenyang, China aut Gao Xianwen College of Information Science and Engineering, Northeastern University, 110819, Shenyang, China aut Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/8(2015-08-01), 2711-2726 0278-081X 34:8<2711 2015 34 34 https://doi.org/10.1007/s00034-015-9981-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-015-9981-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Qi Wenhai College of Information Science and Engineering, Northeastern University, 110819, Shenyang, China aut NATIONALLICENCE 700 1- Gao Xianwen College of Information Science and Engineering, Northeastern University, 110819, Shenyang, China aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/8(2015-08-01), 2711-2726 0278-081X 34:8<2711 2015 34 34