Model conversion of continuous-time uncertain systems via the interval geometric-series method

This brief presents an interval geometric-series approximation method to convert a continuous-time uncertain system to an equivalent discrete-time uncertain model. The system matrices characterizing the state-space representation of the original uncertain systems are assumed to be interval matrices. The exponential matrix-valued function with an interval system matrix is approximated by a rational interval matrix-valued function using the geometric-series approximation method. Then, the desired enclosing interval approximant is obtained by adding an error interval matrix, which accounts for the approximation error, to the rational interval approximant. The model thus constructed is guaranteed to enclose the precise original interval model. The proposed enclosing digital interval model provides less conservative results than the existing Pade enclosing digital interval model. The newly developed digital interval model can be utilized for analysis and design of continuous-time uncertain systems.