\(H_2\) control for the continuous-time Markovian jump linear uncertain systems with partly known transition rates and input quantization (Q473649)

Summary: For a class of continuous-time Markovian jump linear uncertain systems with partly known transition rates and input quantization, the \(H_2\) state-feedback control design is considered. The elements in the transition rates matrix include completely known, boundary known, and completely unknown ones. First, an \(H_2\) cost index for Markovian jump linear uncertain systems is introduced; then by introducing a new matrix inequality condition, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs) for the \(H_2\) control of the Markovian jump linear uncertain systems. Less conservativeness is achieved than the result obtained with the existing technique. Finally, a numerical example is given to verify the validity of the theoretical results.