Multirate output functional observer in linear feedback for systems with unknown inputs

This paper proposes a new method to design a scalar dynamical functional observer based feedback control, for a class of linear sampled-data systems with additive disturbances. The control action consists of the function of system state and disturbance components. The design of the function of state is based on the pole-placement technique and the function of disturbance is for the complete disturbance-counteraction on system performance. This work is based on the combination of functional observer design and multirate output sampling technique. Necessary and sufficient conditions for existence of the proposed controller are derived and the design procedure is given. It is shown that the proposed method relaxes some of the conditions of disturbance decoupled functional observer design, provided that the variation of disturbance in the two consecutive sampling instances is not significant. Numerical example is considered to illustrate the design procedure and its simplicity.