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This study deals with the non-equilibrium transient trajectory shaping problem for non-linear, strict feedback, single-input-single-output systems by a three-stage switching control method. Through this control method, the non-linear system output tracking error can be constrained within a set of properly pre-designed boundaries when it is converging to the equilibrium point. In particular, the three-stage switching control method imposes a constant bound (the first stage), two exponentially converging time-varying functions (the second stage), and a smaller constant bound (the third stage) as the tracking error boundary in each of the three stages, respectively. By designing control laws separately in the corresponding stages, the trajectory of the system tracking error can be assured within the boundaries during transient period. The bound of the control input magnitude can be determined with the respective control law at each stage and consequently establish the tradeoff between system transient performance and the available control resource. Numerical examples are utilised to show the effectiveness of the technique.