A class of near time-optimal nonlinear controllers—the Continuous Proximate Time-Optimal (CPTO) controllers—which involves continuous, rather than discontinuous, nonlinear feedback control functions is introduced. The CPTO controllers give near time-optimal response for large state errors, and provide smooth, stable response with near linear control for small state errors. In this paper, the CPTO controllers for three second-order (two stable and one unstable) plants and one third-order plant are introduced. Complete stability proofs, using the CPTO control law, are given for all the systems considered. It has been shown through the simulation that response times are indeed near time-optimal for all cases considered.

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