Time-delay dependent H_∞ model simplification for singular systems with Markovian jumping parameters

The problem of H_∞ model simplification for singular systems with Markovian jumping parameters and time-delay is investigated. For a given stochastic stable system, our attention is focused on the construction of reduced-order models which guarantee the corresponding error system to be admissible and have a prescribed H_∞ error performance. A robust admissibility condition and a robust bounded real lemma are developed based on which, sufficient conditions for the existence of desired reduced-order models are proposed. Desired reduced-order model can be constructed when the proposed conditions are satisfied. The effectiveness of the proposed model reduction method is illustrated via a numerical example.