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This paper provides a state feedback stabilization approach for nonlinearsystems of relative degree less than or equal to two by rendering themnonlinear negative imaginary (NI) systems. Conditions are provided under whicha nonlinear system can be made a nonlinear NI system or a nonlinear outputstrictly negative imaginary (OSNI) system. Roughly speaking, an affinenonlinear system that has a normal form with relative degree less than or equalto two, after possible output transformation, can be rendered nonlinear NI andnonlinear OSNI. In addition, if the internal dynamics of the normal form areinput-to-state stable, then there exists a state feedback input that stabilizesthe system. This stabilization result is then extended to achieve stability forsystems with a nonlinear NI uncertainty.

Making Nonlinear Systems Negative Imaginary via State Feedback