For most complex dynamic systems, it is not possible to measure all system states in a direct fashion. Thus for dynamic characterization and controller design purposes, it is often necessary to design an observer in order to get an estimate of those states which cannot be measured directly. In this work, the problem of designing state observers for free systems with time periodic coefficients is addressed. For linear time-periodic systems, it is shown that the observer design problem is the duality of the controller design problem. The state observer is constructed using a symbolic controller design method developed earlier using the Chebyshev expansion technique. For the nonlinear time periodic systems, the observer design is investigated using the Poincare´ normal form technique. The local identity observer is designed by using a set of near identity coordinate transformations which can be constructed in the ascending order of nonlinearity. These observer design methods are implemented using a symbolic computational algorithm and several illustrative examples are given to show the effectiveness of the methods.
A Bode sensitivity integral for linear time-periodic systems
