Discretization of MIMO Systems with Nonuniform Input and Output Fractional Time Delays

Input and output time delays in continuous-time state-space systems are treated separately as their effects are encountered before and after the state dynamics. Existing discretization techniques for such systems usually consider the delays to be integer multiples of the sampling time. This work develops a discretization procedure for multi-variable state-space systems with nonuniform input and/or output delays, in which such delays are non-integer multiples of the sampling time. A heat exchanger process example is used to illustrate the advantage of using this technique compared to the discretization approach of rounding the delays to the closest integer multiple of the sampling time. A significant improvement towards the continuous-time response was noted when considering the fractional delays into the discretized model. This discretization improvement is expected to benefit the design and performance of model-based controllers