INSENSITIVE OBSERVERS FOR DISCRETE-TIME LINEAR-SYSTEMS

This paper considers the problem of designing an observer insensitive to system parameter variations in discrete time linear multivariable systems. A K-insensitive observer is defined as an observer that can reconstruct a linear function of the state vector in spite of the variations of system parameters, provided the initial state of the observer is suitably chosen. A deadbeat observer is defined to be an observer that reconstructs the linear function for an arbitrary initial condition of the observer. Then, the existence of the K-insensitive observer is examined, and the class of K-insensitive observers is characterized. A necessary and sufficient condition is derived under which the K-insensitive deadbeat observer can be designed, and a simple algorithm is proposed to design the observer. The resulting observer is shown to be stable. The order of the observer is evaluated. The condition for generic solvability of the problem is also given. © 1979.