A method to avoid the unmeasurable premise variables in observer design for discrete time TS systems

This paper addresses a new method to overcome the unmeasurable premise variables in TS nonlinear discrete time systems for observer design. It is known that a TS system can be obtained directly from a nonlinear one by using the sector nonlinear transformation in a given compact set of the state space. However, this procedure often leads to TS systems having premise variables depending on one or more unmeasurable states. Clearly, the observer design for such a class of TS systems is more difficult than designing observers for TS systems having measured or known premise variables. The objective of this paper is to use the immersion approach before using the sector nonlinear transformation in order to obtain a TS system with measured premise variables. In addition the proposed immersion technique leads to the use of an augmented state vector which first components are directly the state variables of the original system avoiding the computation of an inverse transformation. Example results are provided in order to illustrate the proposed approach.