I need to control a discrete linear system. sliding mode or reference model adaptive control is my favorite. please introduce some paper to learn more about designing a sliding mode and adaptive control of discrete linear systems.
Your question reminded me of a paper by Prof. K. Furuta published in Syst. Contr. Lett. in 1990. Searching with Google using keywords "furuta discrete sliding mode" gives a lot of results. From that list, you can get at least a few full-text publications, for examples,
"Euler’s Discretization of Single Input Sliding-Mode Control Systems by Zbigniew Galias and Xinghuo Yu " is a good paper for designing sliding mode controller .