Optimal time-weighted H2 model reduction for discrete Markovian jump systems

This paper considers the optimal time-weighted H₂ model reduction problem for discrete Markovian jump linear systems (MJLSs). The purpose is to find a mean square stable MJLS of lower order such that the time-weighted H₂ norm of the corresponding error system is minimized for a given mean square stable discrete MJLS. A new notation named time-weighted H₂ norm of discrete MJLS is defined for the model reduction purpose for the first time. Then a computational formula of the time-weighted H₂ norm is given. Based on this formula, a gradient flow method is proposed to solve the optimal time-weighted H₂ model reduction problem. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.