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This paper investigates the problem ofℋ    ∞model reduction for a class of discrete-time Markovian jump linear systems (MJLSs) with deficient mode information, which simultaneously involves the exactly known, partially unknown, and uncertain transition probabilities. By fully utilizing the properties of the transition probability matrices, together with the convexification of uncertain domains, a newℋ    ∞performance analysis criterion for the underlying MJLSs is first derived, and then two approaches, namely, the convex linearisation approach and iterative approach, for theℋ    ∞model reduction synthesis are proposed. Finally, a simulation example is provided to illustrate the effectiveness of the proposed design methods.

mathematical problems in engineering

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℋ</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Model Reduction for Discrete-Time Markovian Jump Systems with Deficient Mode Information

ℋ∞Model Reduction for Discrete-Time Markovian Jump Systems with Deficient Mode Information