Robust control of uncertain singular stochastic systems with markovian switching via proportional-derivative state feedback

This study focuses on the problem of robust control for a class of uncertain singular stochastic Markovian jump systems via proportional-derivative state feedback controllers (PDSFCs). The uncertainties are not only in system matrices, such as state, input and derivative matrices, but also in mode transition rate matrix. New sufficient conditions for the existence of mode-dependent PDSFC are derived as linear matrix inequalities (LMIs) such that the closed-loop singular stochastic system is quadratically normal and quadratically stochastically stable (QNQSS). Especially, another PDSFC referred to be partially mode dependent is also given by a mode-dependent Lyapunov function. Numerical examples are used to show the effectiveness of the proposed methods.