Abstract: This paper addresses the properties of robust stability for sliding mode control in the frequency domain. Conventionally, the sliding mode control is investigated in the time domain. Here, it can be shown that the sliding mode control can be transformed into a Lur’e problem. When considering the uncertainties of system and input matrices, if these uncertainties satisfies the “matching conditions”, then the zero dynamics of sliding surface will not changed; otherwise, the zero dynamics of sliding surfaces will be affected by the un-matched uncertainties and it may becomes unstable. The sliding surface may becomes an unstable manifold. According to circle criterion, a formula is presented here to attain the reaching conditions and the absolute stability of overall system. By the loop transformation and theory, a Linear Matrix Inequality (LMI) is used to determine the reaching conditions and the absolute stability of overall system. Finally, the reaching conditions and the absolute stability of overall system is determined by checking the eigenvalues of a Hamiltonian matrix is also presented here.

Brief Biography of the Speaker:
Chingyei Chung is a professor in the Department of Electronic Engineering, Ming Shin University of Science and Technology, Taiwan Prior to this position, he held various academic positions at Feng Chia University Taiwan and San Francisco State University, USA respectively. He received B.S. from Natl. Chiao Tung University, Taiwan ROC and M.S. degree in electrical engineering from San Jose State University, U.S.A. Also He finished his Ph.D degree in Mechanical Engineering from University of California, Berkeley, USA.
He has four Patents granted by the United State Patent and Trademark Office. In 2003, he is an Distinguished Research Advisor in ABI (American Biographic Institute). His research interests include nonlinear control, nonlinear circuit theory and etc.