On the output feedback control of discrete-valued input systems

Abstract

This paper considers an output feedback control for quantized feedback systems. Our controller focuses on high accuracy control performance for embedded devices with low-resolution AD/DA converters and networked systems with band-limited channels. 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). For certain systems, we provide closed form and numerical solutions for the synthesis problem 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 conditions. The condition reduces to a tractable numerical optimization problem. Second, a closed form solution of optimal controller for the quantized feedback system is clarified within the invariant set framework. Third, we discuss the controller synthesis conditions which are characterized by the transmission zero property. Finally, to verify the validity of our method, numerical examples are presented and then the contributions related to the existing dynamic quantizer synthesis are clarified.