Model reduction on Markovian jump systems with partially unknown transition probabilities: balanced truncation approach

In this study, the problem of model reduction based on balancing is investigated for both discrete- and continuous-time Markovian jump linear systems with partially unknown transition probabilities. By balancing transformation, the reduced-order model with the same structure as that of the original one is obtained by truncating the balanced model. For the obtain reduced order model, stability property is preserved under simultaneous balanced truncation. An upper bound of the model reduction error is guaranteed in the sense of a perturbation operator norm. Finally, two illustrative examples are provided to show the feasibility and effectiveness of the method presented in this study.