Quantum level for stochastic discrete-time sliding modes

This paper considers a feedback control system where a plant is actuated by a quantized control. The control is obtained by the quantization of measurements which are assumed to be disturbed by an additive wideband Gaussian noise in the feedback loop. In the continuous-time case, the nonlinear control may cause the system to behave as a variable structure system (VSS) which exhibits a sliding mode on the sliding surface. In the discrete-time case, however, the system may or may not yield an associated sliding mode by discretizing the controller in the continuous-time case. It provides the motivation to consider the quantum levels in a uniform quantizer so that the discrete-time sliding mode has the same behavior as the continuous-time sliding mode. Thus, the sliding controller design scheme for continuous-time quantized control systems may be extended to discrete-time systems.