A Parametric Method of Linear Functional Observers for Linear Time-varying Systems

This paper considers the design of a Luenberger observer to estimate the linear multiple states functional for linear time-varying (LTV) systems. Based on the solutions to a type of full actuated homogeneous generalized Sylvester matrix equations and the conditions for the existence of observers for LTV systems, general parametric solutions to Luenberger functional observers are established. With the proposed approach, the functional observers can be achieved at desired convergence rate of the observation error, and also without any particular transformation for LTV systems. Finally, a numerical example shows the feasibility and effectiveness of the proposed parametric design method for the functional observers in LTV systems.