Model conversions of uncertain linear system via the interval tuning bilinear approximation method

This paper presents a new tuning bilinear approximation method together with the interval arithmetic operation to convert a continuous-time (discrete-time) uncertain system to an equivalent discrete-time (continuous-time) uncertain model. Based on the bilinear approximation method, we induct one parameter for tuning the error bound between the exact and approximate uncertain system matrices. The bounds of interval system matrices via the proposed interval tuning bilinear approximation method are narrower than those of the existing interval bilinear and the interval pade approximation methods⁽¹⁾. The resulting interval models (the enclosing interval models) are able to tightly enclose the exact uncertian models. Also the approximate discrete-time interval solution is able to tightly enclose the exact interval solution of the continuous-time uncertain state-space equation. The proposed method will be helpful for analysis and synthesis of uncertain systems.