Stabilization of discrete-time quantized control systems

This paper considers a discrete-time linear time-invariant feedback control system where an unstable plant is actuated by a quantized controller and the measurements are disturbed by an additive wideband noise in the feedback loop. The quantized control may cause the discrete-time system to be modeled as variable structure under the existence and convergence conditions of a quasi-sliding mode. The control guides the system to the origin via a quasi-sliding mode, however, it may not constrain the system to the origin. Linear stabilizing controllers near the origin are investigated, and in the steady state the performance of the stabilized system is examined via a quadratic performance index. Numerical examples are presented and discussed as an illustration.