ℋ_∞ model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information

This paper investigates the problem of ℋ_∞ model reduction for a class of continuous-time Markovian jump linear systems with incomplete statistics of mode information, which simultaneously considers the exactly known, partially unknown and uncertain transition rates. By fully utilising the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for ℋ_∞ performance analysis is first derived, and then two approaches, namely, the convex linearisation approach and the iterative approach, are developed to solve the model reduction problem. It is shown that the desired reduced-order models can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a sequential minimisation problem subject to LMI constraints, which are numerically efficient with commercially available software. Finally, an illustrative example is given to show the effectiveness of the proposed design methods.