On the output feedback control of discrete-valued input systems

This paper considers an output feedback control for quantized feedback systems. Our controller provides high accuracy control performance for embedded devices with low-resolution ADIDA converters. For a certain system, we provide closed form and numerical solutions for the synthesis problem. The synthesis problem we address is the simultaneous synthesis of the nominal controller and the delta-sigma modulator (where the modulators are called the dynamic quantizers). Our approach is based on the invariant set analysis and the LMI technique. First, this paper proposes a synthesis condition that is recast as a set of matrix inequality condition. The condition reduces to a tractable numerical optimization problem. Second, a closed form solution of an optimal controller for the quantized feedback system is clarified within the invariant set framework. Finally, we discuss the controller synthesis conditions which are characterized by the transmission zero property.