Controlling the Ćuk Converter Using Polytopic Lyapunov Functions

In this brief, the Ćuk dc/dc converter is controlled by a switching sequence based on the values of a polytopic Lyapunov function. In particular, the switching control signal is computed using a Lyapunov function which has polytopic level sets and it is not everywhere differentiable. The problem of not everywhere differentiability is handled using the Filippov's approach for discontinuous differential equations. The main advantage of the presented control design approach is that it provides exact computation of the state variables' ripple values which could not be obtained with previously used quadratic Lyapunov functions. The implementation particularities of the approach are illustrated and verified using a number of simulations.