Constrained switching stabilization of a dc-dc boost converter using piecewise-linear Lyapunov functions

This paper describes a new methodology for designing robust and efficient control laws for power converters. In addition to guaranteed closed-loop robust stability, the proposed design is capable of addressing a number of further key issues, i.e. low complexity of the implementation, accurate nonlinear dynamics incorporation, nonconservative handling of hard state and control constraints, and robustness to supply voltage variations and setpoint changes. The control design is of a set-theoretic nature. The iterative algorithms used for controller generation are based on the ray-gridding approach, that generates piecewise-linear Lyapunov functions and corresponding controlled invariant polytopes, induced by systematic conic decompositions of the state-space and state-dependent switching control actions. The proposed technique is evaluated on a boost converter case study. Simulation results in the MATLAB/SIMULINK™ environment are reported. The bifurcation behaviour of the system is further studied by numerical and analytical nonlinear stability analysis.