A frequent feature of numerical partial and ordinary differential equations, numerical solutions of convolution-type integral equations, stationary retrogressive time series in statistics, minimal realization
problems in control theory, system identification problems in signal process, and image restoration problems, Toplitz systems are important to mathematics, computing and engineering.
A simple reduction to determine a minimal realization of the system is introduced.
Thus, deleting these rows and columns yields the minimal realization of the gasifier system.
Before performing any numerical operation using the resulting state space minimal realization matrices, a numerical pre-conditioning on these matrices was carried out, since the gasifier system is not well conditioned as mentioned before.