R-composition of quadratic Lyapunov functions for stabilizability of linear differential inclusions

A novel state feedback control technique to stabilise linear differential inclusions through composite quadratic Lyapunov functions is presented. By using a gradient-based control technique, the minimum effort control is composed through intersection and union operations, derived from the theory of R-functions. While conventional min and max compositions are recovered as a special case, it is shown that smoother sublevel sets and everywhere differentiability are obtained tuning the composition parameter. Examples of both intersection and union compositions are provided to show that intermediate control performances in terms of convergence time are obtained, while improved performances in the control signal can be achieved.