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Stabilizations of strong nonlinear system via novel nonlinear state observers

A nonlinear (linear, bilinear and nonlinear) reduced order state observer which is grobally asymptotically stable is derived. Then an unstable nonlinear system which can not be stabilized(here we call it a strong nonlinear system) is stabilized by feeding back the reconstructed states. In this stabilization a kind of separation theorem is introduced by using eventual stability theories. This useful observer, however, may be constructed only for a restricted class of nonlinear systems. Therefore a nonlinear identity state observer although which is only locally stable, is proposed. Finally a stabilization, strategy by this observer is presented.