Abstract
A nonlinear control system with uncertain dynamics described by a single ordinary differential equation with scalar control and available state is given. Based on knowledge of upper and lower estimates of the unknown dynamics, we show that the system can be transformed to an asymptotically equivalent linear model (arbitrarily fixed) described by a single linear ordinary differential equation of the same order, by using an (explicitly described) discontinuous feedback control law of variable structure type.The linear behaviour is obtained up to an (arbitrarily fast) exponentially decaying error term.
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