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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 2416193, 11 pages
Research Article

Controller Design for Asynchronous Hybrid Systems with Multiple Delays

Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou, Zhejiang 310027, China

Received 17 December 2015; Revised 27 June 2016; Accepted 11 July 2016

Academic Editor: Masoud Hajarian

Copyright © 2016 Xiaoqiang Sun and Weijie Mao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Solutions for the synthesis problems of asynchronous hybrid systems with input-output delays are proposed. The continuous-time lifting approach of sampled-data systems is extended to a hybrid system with multiple delays, and some feasible formulas to calculate the operators of the equivalent discrete-time (DT) system are given. Different from the existing methods derived from symplectic pair theory or by state augmentation, a Lyapunov-Krasovskii functional to solve the synthesis problem is explicitly constructed. The delay-dependent stability conditions we obtained can be described in terms of nonstrict linear matrix inequalities (LMIs), which are much more convenient to be solved by LMI tools.