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This article proposes a new strictly bounded real lemma (BRL) for continuous‐time singular Markovian jump systems (SMJSs) in terms of strict linear matrix inequalities (LMIs). While the previous studies have been done for SMJSs that do not have a path from disturbances to desired output, the proposed BRL covers SMJSs with disturbance‐contaminated output by introducing additional free matrix variables. Based on the proposed BRL, the sufficient condition for state‐feedback stabilization is successfully obtained in terms of strict LMIs. The result leads to find the minimal ℋ∞ performance by solving the optimization problem subject to the suggested LMIs. Two examples show the less conservatism of proposed method compared with the previous work. [ABSTRACT FROM AUTHOR]

This paper considers H ∞ filtering for continuous-time singular Markovian jump systems (SMJSs). While the existing researches in the literature suggested only sufficient conditions in terms of strict or non-strict linear matrix inequalities (LMIs) for sub-optimal H ∞ filtering, this paper successfully derives a necessary and sufficient condition in terms of strict LMIs for optimal H ∞ filtering. First, the necessary and sufficient condition that guarantees the stochastic admissibility of the filtering error system is obtained in terms of matrix inequalities. To reformulate it into strict LMIs, the congruence transformation by specially designed matrices is used. Two numerical examples show the validity of proposed H ∞ filtering. [ABSTRACT FROM AUTHOR]

Summary: This paper considers a dynamic output‐feedback H ∞ control for continuous‐time singular Markovian jump systems, whereas the existing research studies in literature focused on state‐feedback or static output‐feedback H ∞ control. While they have only provided the sufficient conditions, this paper successfully obtains the necessary and sufficient condition for the existence of the dynamic output‐feedback H ∞ control. Furthermore, this condition is expressed with linear matrix inequalities by the so‐called replacement technique. Two numerical examples show the validity of the resulting control. [ABSTRACT FROM AUTHOR]