Matching conditions for stability analysis of nonlinear feedback control systems

The differential geometry approach for exact input-output linearizable nonlinear systems usually results in a complicated nonlinear controller that is difficult to implement. To overcome this difficulty, we propose to approximate the nonlinear controller by a canonical piecewise linear expression within an allowable error bound. This design procedure can reduce a tremendous amount of computation in the design and the synthesis. The resulting controller turns out to be fairly simple in general and can achieve many performance specifications. Some sufficient conditions for guaranteeing the closed-loop system stability using this controller design method is derived in the present paper. An application to a chemical reactor system is also briefly discussed.