12 Asian Journal of Control, Vol. 8, No. 1, pp. 12-20, March 2006 Manuscript received April 15, 2005; accepted November 7, 2005. Yong Feng and Xuemei Zheng are with Department of Elec- trical Engineering, Harbin Institute of Technology, Harbin 150001, China (e-mail: yfeng@hit.edu.cn, xuemeizheng_hrb@ sina.com). Xinghuo Yu is with School of Electrical and Computer En- gineering, Royal Melbourne Institute of Technology, Mel- bourne, VIC 3001, Australia (e-mail: x.yu@rmit.edu.au). This paper was supported by the National Natural Science Foundation of China (No.60474016) and the Scientific Re- search Foundation for Returned Overseas Chinese Scholars, State Education Department of China. SECOND-ORDER TERMINAL SLIDING MODE CONTROL OF INPUT-DELAY SYSTEMS Yong Feng, Xinghuo Yu, and Xuemei Zheng ABSTRACT This paper proposes a second-order terminal sliding mode control for a class of uncertain input-delay systems. The input-delay systems are firstly converted into the input-delay free systems and further converted into the regular forms. A linear sliding mode manifold is predesigned to represent the ideal dynamics of the system. Another terminal sliding mode manifold surface is presented to drive the linear sliding mode to reach zeros in finite time. In order to eliminate the chattering phenomena, a second-order sliding mode method is utilized to filter the high frequency switching control signal. The uncertainties of the systems are analysed in detail to show the effect to the systems. The simulation results validate the method presented in the paper. KeyWords: Delay systems, time delay, sliding mode control, system design. I. INTRODUCTION Time-delay effect is very common in many practical applications such as aircraft, chemical and biological reac- tors, process control systems, rolling mills, automotive engines, manufacturing systems, communication network and economics, etc. Time-delay appears either in the state, or the control input, or the measurements of systems. Time- delay often significantly degrades the control performance of systems or even destabilizes the systems. Therefore, the issues of controlling the time-delay systems are of both theoretical and practical importance. There are three kinds of time delay systems: the sys- tems with state delay, the systems with input delay, and the systems with simultaneous state and input delays. Although some engineering systems exhibit delay in the states, delay in the input variables is particularly pervasive in numerous applications, such as chemical processing, for example [2]. This paper is mainly concentrated on the issue of the con- trol of the input-delay systems. The control of input-delay systems has received much attention in the literature in the last few years. Many re- search results, including both delay-independent and delay- dependent results, have been obtained based on either the Laypunov theory of stability or frequency domain consid- erations [1]. A main method is to use a transformation that converts the original system into a delay-free form, such as a sliding mode control design for a class of uncertain input- delay systems [2], and a sliding mode control scheme to ensure the asymptotic stability of a linear system with de- lay in both the input and state variables [3]. For the robust stabilization of uncertain input-delay systems, a sliding mode control and a sliding mode control with uncertainty adaptation were proposed by using a predictor to compen- sate for the input delay of the system and the adaptation scheme respectively [4,5]. For systems with a single and pure input lag, based on state-space analysis, mixing a finite-dimensional and an abstract evolution model, the standard H ∞ problem was resolved [6]. The stability crite- rion of the closed-loop system was derived in terms of lin- ear matrix inequalities (LMIs) [7]. A sub-optimal second order sliding mode control law for a double integrator sys- tem with delayed input was investigated [8]. A disturbance