Model conversions of uncertain linear systems using interval multipoint Pade approximation

Many dynamic systems and industrial control processes can be represented by a multirate sampled-data uncertain system, which consists of a continuous-time uncertain subsystem and a multirate discrete-time uncertain subsystem. The uncertainties in these systems arise from unmodeled dynamics, parameter variations, sensor noises, actuator constraints, etc. As is the common practice the sampled-data uncertain system needs to be converted to a purely continuous-time or discrete-time uncertain model, so that the well-established analysis and design methods in the continuous-time or discrete-time domain can be directly applied to the equivalent model. This paper presents a new interval multipoint Pade approximation method for converting a continuous-time (discrete-time) uncertain linear system to an equivalent discrete-time (continuous-time) uncertain model. The system matrices characterizing the state-space descriptions of the original uncertain systems are represented by interval matrices. Using the approximate uncertain models obtained based on interval analysis and multipoint Pade approximation the dynamic states of the resulting models have been shown to be able to closely match those of the original uncertain systems for a relatively longer sampling period.