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Power-electronic converters are intrinsically nonlinear. This paper proposes a Lyapunov approach to analysis and design of a class of nonlinear systems arising from power-electronic converters. The system has a bilinear term as the product of the state and the input-the duty cycle, which is subject to strict constraint (or saturation). The nonlinearities and the input saturation are considered in this paper by using piecewise-quadratic Lyapunov functions and by describing the system with a piecewise-linear differential inclusion. The problems considered include controller design for robust stability, and estimation of stability region and tracking domain. These analysis and design problems are converted into numerically efficient optimization algorithms involving linear-matrix inequalities (LMIs). A buck-boost dc-dc converter is used to demonstrate the proposed methods. The optimization results show that a simple state-feedback law can be constructed to achieve practically global stabilization and tracking, which is theoretically confirmed by the Lyapunov approach. An experimental buck-boost converter is constructed to verify the tracking of a square reference varying almost between the upper and the lower limit.