A team algorithm for robust stability analysis and control design of uncertain time-varying linear systems using piecewise quadratic Lyapunov functions

We introduce the use of team algorithms using piecewise quadratic simultaneous Lyapunov functions for robust stability analysis and control design problems involving uncertain time-varying linear systems. The objective is to employ robust stability criteria that are less conservative than the well-known quadratic stability approach. The use of piecewise quadratic Lyapunov functions leads to a non-convex optimization problem, which is solved by a team algorithm that is a combination of a genetic algorithm with an interior-point method for linear matrix inequalities. Numerical examples are given, showing the advantages of the proposed solution.