Discretization of cascaded continuous-time controllers and uncertain systems

This paper presents a new method for the digital modeling of a continuous-time uncertain system and a new method for the digital redesign of a sampled-data uncertain system. The system matrices characterizing the state-space representation of the original uncertain system are assumed to be interval matrices. The Chebyshev quadrature formula together with the interval arithmetic are used for the digital interval modeling, and a dual concept of digital interval modeling is utilized to discretize a predesigned cascaded analog controller for robust digital control of a continuous-time uncertain system. Using the newly developed digital interval models and digitally redesigned controllers, the resulting dynamic states of the digitally controlled sampled-data uncertain systems are able to closely match those of the originally analogously controlled continuous-time uncertain systems for a relatively longer sampling period.