ℓ<inf>2</inf>–ℓ<inf>∞</inf> proportional–integral observer design for systems with mixed time-delays under round–robin protocol

Abstract

In this article, the design problem of ℓ<inf>2</inf>–ℓ<inf>∞</inf> 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<inf>2</inf>–ℓ<inf>∞</inf> disturbance attenuation/resistance capacity. Finally, a simulation example is exploited to verify the validity of the proposed observer design method.