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 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.