Stabilization of stochastic quantized control systems

This paper considers a feedback control system where a plant is actuated by a quantized control. The measurements are assumed to be disturbed by an additive wideband Gaussian noise. The nonlinear control is obtained by the quantization of the measurements and it may cause the system to be variable structure in the presence of the noise. Variable structure systems disturbed by the noise exhibit sliding modes on the switching manifold. When the system is unstable, linear optimal controls using linear-quadratic-Gaussian (LQG) formulation are investigated to stabilize the system in a region around the origin while the quantized control guides the system to the region. The performance and behavior of the stabilized systems are examined via a quadratic performance index in the steady state.