Improved H_∞ control for singular Markovian jump systems via dynamic output-feedback

This paper investigates the H_∞ output-feedback admissibilization problem for singular Markovian jump systems (SMJSs) subject to disturbance-contaminated performance outputs. Most existing H_∞ control results for SMJSs rely on the assumption that external disturbances do not directly affect the performance outputs, which significantly restricts their applicability. To address this limitation, a synthesis framework is developed that explicitly incorporates disturbance-to-output channels within the SMJS model. By introducing specially structured slack variables, the intractable nonconvex synthesis conditions arising from bilinear couplings between controller gains and Lyapunov variables are transformed into strict linear matrix inequalities. The resulting conditions enable the systematic design of dynamic output-feedback controllers while guaranteeing admissibility and prescribed H_∞ performance. Two practical examples are provided to demonstrate the effectiveness of the proposed method. In these examples, the method handles disturbance-contaminated performance outputs that an existing output-feedback approach cannot handle. It also attains smaller attenuation levels than an existing state-feedback design.