Abstract
Finite-time control and fault detection are treated simultaneously as a single problem for a class of continuous-time singular Markovian jump delay systems. To develop the objectives for both control and detection, mode-dependent fault detection filters and dynamic feedback controllers were designed for a certain set of performance indices. Based on the average dwell time approach and using some novel integral inequalities, new sufficient conditions for the presence of a fault detection/controller unit are presented as a set of linear matrix inequalities. This problem is formulated as a finite-time $$H_\infty $$ optimization problem, and both the stochastic finite-time stability and fault detection filter are analyzed, employing a switching control approach. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.
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