Semi-Global Sampling Control for Semi-Markov Jump Systems With Distributed Delay
Ning Zhang, Shunjie Huang, Luheng Ning, Wenxue Li
Abstract
In this paper, the semi-global exponential stability of semi-Markov jump systems with distributed delay under semi-global sampling control is studied. Besides, a new definition of functional derivative associated with the semi-Markov jump is given. By using the global exponential stability of semi-Markov jump system with distributed delay under global continuous control, incorporation with the inequality technique, the semi-global exponential stability criteria of semi-Markov jump system with distributed delay under semi-global sampling control are given, including Lyapunov-type theorem and coefficient-type theorem. Eventually, an application about a class of oscillator systems combining the theoretical results is discussed and the corresponding numerical example is presented to demonstrate the effectiveness of the theoretical results. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Sampling control has gained broad attention for its cost-saving and reliability. In some practical sampling control systems, due to the inner property, they can not achieve stability in global scope but only in local range and the converge speed depends on the initial value. In this paper, we give a novel definition of horizontal movement of the segment function and Dini’s derivate of the constructed functional is presented basically, which is adapted to more than the solution of the systems and is of much flexibility. The maximum sampling interval is provided to make the sampling control systems keep stable. And the results provide a reference for the semi-global stability of oscillator systems with semi-Markov jump under sampling control.