Balanced Performance Preserving Model Reduction for Uncertain Semi-Markovian Jump Systems

This paper is concerned with the model reduction (MR) problem for continuous-time phase-type semi-Markovian jump systems (PH-SMJSs) based on balanced truncation method. The time-varying delay in states is considered via Wirtinger-based integral inequality and the parameter uncertainties are assumed to be randomly occurring. By utilizing the generalized output and input dissipation inequalities, the generalized gramians are solved. And the balanced realizations of the original PH-SMJSs are yielded according to the abilities of the controllability and observability. Then the low-order models are found by state truncation technique. Furthermore, the balanced performances of the original PH-SMJSs are preserved in the low-order systems. A numerical example is conduced to clarify the effectiveness of the proposed balanced performance preserving MR method for SMJSs.