Asynchronous dissipative control for networked time-delay Markov jump systems with event-triggered scheme and packet dropouts

Abstract

Abstract This paper is concerned with asynchronous dissipative control for a class of networked time-delay Markov jump systems with event-triggered scheme and packet dropouts. To reduce communication consumption, an event-triggered transmission scheme is introduced. The phenomenon of packet dropout during the communication between the controller and the actuator is described by the Bernoulli model. The designed dissipative controller is asynchronous with the physical plant, which is described by a hidden Markov model. Based on a mode-dependent Lyapunov–Krasovskii function, a sufficient condition for the closed-loop control system to be stochastically stable and strictly $$(\mu ,\vartheta ,\upsilon ){-}\gamma$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>μ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ϑ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>υ</mml:mi> <mml:mo>)</mml:mo> <mml:mo>-</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> -dissipative is obtained. Furthermore, the design of dissipative controller is simplified by using matrix scaling and slack matrix techniques. Finally, a robotic arm system is used as an example to verify the effectiveness of our proposed design method.