H 2 Control for the Continuous-Time Markovian Jump Linear Uncertain Systems with Partly Known Transition Rates and Input Quantization

For a class of continuous-time Markovian jump linear uncertain systems with partly known transition rates and input quantization, the H2 state-feedback control design is considered. The elements in the transition rates matrix include completely known, boundary known, and completely unknown ones. First, an H2 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 H2 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.