Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
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The problem of observing the states of two tandem-connected linear stationary systems is considered. It is shown that if the tandem systems are observable then the tandem system observer can be composed of two separate systems, each the same order as the corresponding system being observed. Let the state vector of the input system be denoted by d and the state vector of the output system be denoted by x. (See Fig. 1.) The decoupled observer is based upon a Luenberger observer designed for the output system as if d(t) were zero for all time. A second observer is then added which observes d(t). The output of these two observers is then combined to form the observed x(t) with d(t) nonzero. (See Fig. 2.) An advantage of this decoupled observer is that if the input system is changed, then only one of the two observers must be redesigned. An example which demonstrates the construction and operation of this observer is discussed.