l2-l∞ proportional-integral observer design for systems with mixed time-delays under round-robin protocol

In this article, the design problem of l(2)-l(infinity) proportional-integral observer (PIO) is investigated for a class of discrete-time systems with mixed time-delays. The mixed time-delays comprise both the discrete time-varying delays and infinitely distributed delays. The round-robin protocol (RRP) is employed to schedule the data transmissions from the sensors to the observer so as to mitigate the communication burden and prevent the data collisions. A novel PIO is developed whose observer gain is dependent on the data transmission order as a reflection of the effects induced by the RRP scheduling. By resorting to the token-dependent Lyapunov functional and the matrix inequality technique, the desired PIO is designed with exponentially stable error dynamics of the state estimation and guaranteed l(2)-l(infinity) disturbance attenuation/resistance capacity. Finally, a simulation example is exploited to verify the validity of the proposed observer design method.