Model conversion of uncertain linear systems with input time-delay via the interval bilinear approximation method

This paper presents a method for model conversion of a continuous-time (discrete-time) uncertain linear system with input time-delay to an equivalent discrete-time (continuous-time) uncertain linear time-delay model. The bilinear approximation method and interval arithmetic operations are proposed for converting continuous-time (discrete-time) uncertain input time-delay models to equivalent discrete-time (continuous-time) uncertain input time-delay models. Here, we also present a method to estimate tighter error bounds of discrete-time (continuous-time) structured uncertainties based on the given continuous-time (discrete-time) structures uncertainties. By applying the above proposed methods, the converted model tightly encloses the original system; consequently, the analysis and design can be carried out using the obtained models instead of the original systems. An example is given to demonstrate the effectiveness of the proposed method.