H∞ performance for delayed singular nonlinear Markovian jump systems with unknown transition rates via adaptive control method

Abstract

Abstract We work on the investigation of the H ∞ performance for uncertain stochastic singular Markovian jump systems with both nonlinear external disturbance and general unknown transition rates (TRs) in this paper. There exist uncertainties in both parameters and TRs. Every transition rate could be totally unavailable or only its estimated value is available. With a generalized H ∞ disturbance attenuation level γ , some robust controllers are designed such that the delayed singular Markovian jump system is stochastically admissible. The novel controllers designed in this paper consist of an adaptive controller and a linear controller. Moreover, some sufficient linear matrices inequalities (LMIs) conditions are provided according to Lyapunov stability theory and It o ˆ ’s differential formula. Finally, an example is presented to demonstrate our main results.