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In this paper, a simple calculation method to derive the Luenberger observer for linear time-varying discrete systems is presented. For this purpose, the simple design method of the pole placement for linear time-varying discrete systems is proposed. It is shown that the pole placement controller can be derived simply by finding some particular ”output signal” such that the relative degree from the input to this new output is equal to the order of the system. Using this fact, the feedback gain vector can be calculated directly from plant parameters without transforming the system into any standard form. Then, this method is applied to the design of the observer, i.e., because of the duality of linear time-varying discrete system, the state observer can be derived by simple calculations.

SIMPLE DERIVATION OF A STATE OBSERVER OF LINEAR TIME-VARYING DISCRETE SYSTEMS