Stabilization of nonlinear sandwich systems via state feedback – Discrete-time systems Xu Wang 1, * , Anton A. Stoorvogel 2 , Ali Saberi 1 , H˚ avard Fjær Grip 3 and Peddapullaiah Sannuti 4 1 School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164-2752, USA. 2 Department of Electrical Engineering, Mathematics, and Computing Science, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. 3 Department of Engineering Cybernetics, Norwegian University of Science and Technology, O.S. Bragstads plass 2D, NO-7491 Trondheim, Norway. 4 Department of Electrical and Computer Engineering, Rutgers University, 94 Brett Road, Piscataway, NJ 08854-8058, USA. SUMMARY A recent paper [1] considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched between linear systems. We focus first on single-layer sandwich systems, which consist of a single saturation sandwiched between two linear systems. For such systems, we present necessary and sufficient conditions for semi-global and global stabilization by state feedback, and develop design methodologies to achieve the prescribed stabilization. We extend the results to single-layer sandwich systems subject to additional actuator saturation. Finally, we discuss further extension to general multi-layer sandwich systems with an arbitrary number of saturations sandwiched between linear systems, both with and without actuator saturation. The design methodologies can be viewed as extensions of classical low-gain design methodologies developed during 1990’s in the context of stabilizing linear systems subject to actuator saturation. Copyright c  2010 John Wiley & Sons, Ltd. 1. Introduction Physical systems are typically made up of interconnected subsystems, some of which are well- characterized as linear, and some of which are distinctly nonlinear. Many systems can therefore be described as an interconnection of separable linear and nonlinear parts. A common type of structure consists of a static nonlinearity sandwiched between two linear systems. One of the ubiquitous static * Correspondence to: Xu Wang, School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164-2752, USA. xwang@eecs.wsu.edu Contract/grant sponsor: NAVY grants; contract/grant number: ONR KKK777SB001,ONR KKK760SB0012 Contract/grant sponsor: The Research Council of Norway