Stability criteria for uncertain linear time-varying systems

In this paper robust stability of continuous linear time-varying systems is addressed based on Lyapunov functions which are constructed by max-composition of continuously differentiable functions. The resulting Lyapunov functions are continuous but not necessarily differentiable and no individual component needs to be positive definite. When the components are quadratic functions it will be possible to prove robust stability of systems which fail the classic quadratic stability test. The resulting conditions are matrix inequalities which are linear after choosing a set of tuning parameters. The robust stability condition is also extended to provide upper-bounds on integral performance measures.