Nonlinear Analysis: Hybrid Systems 24 (2017) 83–99 Contents lists available at ScienceDirect Nonlinear Analysis: Hybrid Systems journal homepage: www.elsevier.com/locate/nahs Robust output feedback sliding mode control for uncertain discrete time systems Behrooz Rahmani Control Research Lab., Department of Mechanical Engineering, Yasouj University, 75914-353 Yasouj, Iran article info Article history: Received 19 January 2016 Accepted 14 November 2016 Keywords: Robust sliding mode control Mismatched uncertainty Kalman filter Output tracking and model following Linear matrix inequalities abstract This paper proposes a robust output feedback controller for a class of uncertain discrete- time, multi-input multi-output, linear, systems. This method, which is based on the combination of discrete-time sliding mode control (DTSMC ) and Kalman estimator, ensures the stability, robustness and an output tracking against the modeling uncertainties at large sampling periods. For this purpose, an appropriate structure is considered for sliding surface and the Lyapunov theory for the mismatched uncertain system is then used to design its parameter. This problem leads to solve a set of linear matrix inequalities. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show the effectiveness of the proposed method in the presence of parameter uncertainties and external disturbances at large sampling periods. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction In recent years, sliding mode control (SMC ) has been extensively developed for continuous-time (CT ) systems [1]. Its attractive features such as good tracking properties and robustness against a large class of perturbations or model uncertainties and chaotic behavior encourage the researchers to apply SMC to a variety of practical engineering systems such as robot manipulators, underwater vehicles, spacecrafts, and flexible structures [2–8]. On the other hand, due to the rapid progress of digital signal processor (DSP ) boards and industrial computers, digital controllers have been paid more attention, recently. In this way, computers or DSP boards are used for the control of CT plants. This configuration which is named as sampled-data control systems, results in the ease of implementation, more flexibility to change, and low installation cost compared with the traditional analog control systems. However, despite such important advantages, the actual implementation of such systems, gives rise to new theoretical challenges in the SMC controller design due to coexisting of discrete-time (DT ) and CT signals. As CT sliding mode control can maintain the states of a system on the sliding surface, discrete-time sliding mode control (DTSMC ) try to remain the states in the vicinity of the sliding surface. This is due to the fact that control signals are generated by DTSMC at sampling instants and are held fixed over the entire sampling period. Compared with the large amount of publications on SMC for CT systems, the DTSMC is in the infancy. In order to compensate the sampling negative effects on the closed-loop performance, two basic approaches have been proposed. In the first technique which is named as digital redesign or indirect method, the DTSMC is obtained by discretization of a predesigned continuous time SMC (CTSMC ). For this purpose, the conventional discretization methods, such as the zero-order hold (ZOH)-equivalent and Euler’s are used; for example in [9–14]. But, in such indirect methods, the behavior of the resulting closed-loop system is not considered in the design procedure. This may lead to a periodic behavior and even unstable response in certain cases [11] and in order to preserve the closed-loop stability and tracking E-mail address: b_rahmani@yu.ac.ir. http://dx.doi.org/10.1016/j.nahs.2016.11.004 1751-570X/© 2016 Elsevier Ltd. All rights reserved.