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We study the solution properties of a family of inverted pendulum systems driven by odd periodic forcing. Using the Schauder fixed point theorem, we show that the inverted pendulum with an odd periodic driving acceleration at the pivot always possesses an odd periodic solution. Fundamental to the production of good estimates is the development of a Green's function for an unstable harmonic oscillator...
For a class of multi-input multi-output nonlinear systems a technique of designing stabilizing compensators is given; the nonlinearities in the systems can possibly have memory. The linearizing effect of large compensator gain is shown for the class of systems under consideration. Furthermore, stability analysis for this class of systems is discussed.
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