The design and implementation of a time-varying observer and an EMA controller for linear systems

A method is developed for the design of a class of observers which will handle time-varying linear systems. The time-varying linear system is stabilized by steering the extended-mean values of all closed-loop ED-eigenvalues into the left-half plane, so that bounded-input bounded-output stability of the closed-loop system is guaranteed. This principle is analogous to the eigenvalue (pole) placement assignment idea used for time-invariant linear systems. The eigenvalues of the coefficient matrix of the observer can be placed arbitrarily. This method leans to a system of time-varying differential equations for the determination of the elements of the T matrix using the transformation z=Tx. The results presented are to be used as an alternative to frozen-time analysis of missile systems. However, the observer used in conjunction with the EMA controller provides a design which could be used to control any system governed by time-varying linear equations.