Observer-based finite-time asynchronous control for a class of hidden Markov jumping systems with conic-type nonlinearities

An observer-based finite-time asynchronous H ∞ control law is designed for a class of hidden Markov jumping systems with non-linearities and external disturbances. The non-linearities satisfy the conic-type constraint condition that lies in a known hypersphere with an uncertain centre. The non-synchronisation phenomenon between the system modes and observer/controller modes is modelled by a hidden Markov model. By means of the proper stochastic Lyapunov–Krasovskii functional method, a sufficient condition is obtained to guarantee the stochastic finite-time boundedness of the corresponding argument error dynamic systems with a satisfied H ∞ disturbance rejection level. Finally, the feasibility and validity of the main results is illustrated through a pratical example related to the DC motor.