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Input-to-state stability of a class of Lur'e descriptor systems


Correspondence to: Chunyu Yang, School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou, 221116, P.R. China.



This paper considers a class of Lur'e descriptor systems (LDS) subject to exogenous disturbances. The concept of input-to-state stability (ISS) is generalized to descriptor systems. Such a notion characterizes the robust stability of the full state of the systems. Based on the conventional ISS theory, a sufficient condition expressed by linear matrix inequalities (LMIs) for the LDS to be ISS is derived. It is further shown that this condition also guarantees a special class of LDS to be of index one. Then, a state feedback controller is designed to make the closed-loop system ISS. Finally, an example is given to illustrate the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.