Observer-based H_∞ control design for singular switching semi-Markovian jump systems with random sensor delays

This paper studies the problem of H_∞ control design for a class of singular switching semi-Markovian jump systems, in which the transition rates of jumping process are uncertain and the output measurements suffer from random sensor delays. Firstly, a Luenberger observer is designed to estimate the system state components, based on which an error dynamic is obtained. Then, stochastic stability analysis for the overall closed-loop system is given based on the upper and lower bounds of transition rates. Further, the state feedback controller gain matrices are given by solving a set of sufficient conditions in terms of strict linear matrix inequalities (LMIs), which also guarantee the closed-loop system to be stochastically stabilizable and has a prescribed H_∞ performance index γ. Finally, a numerical example is provided to verify the effectiveness of the obtained result.