An H∞ adaptive observer design for linear descriptor systems

This paper is devoted to the design of an H_∞ adaptive observer for a class of linear descriptor systems in order to estimate simultaneously the system states and its parameters. Based on a mathematical transformation on the system, a new method is presented in order to get an augmented measure matrix from which the observer is built. The existence conditions of the observer are given through matrices equations and are so easily verified via rank conditions. The H_∞ observer is then designed using a mathematical parameterization via LMI, in order to ensure the minimization of the disturbances effects on the observation errors. A numerical example is then given to illustrate the design procedure.