Extremal solutions and extremal norms of linear differential inclusions of order three

Linear differential inclusions arising in the theory of absolute stability of feedback systems with two time-varying sector nonlinearities are considered. It is shown that under controllability/observability assumptions in the case of zero Lyapunov exponent all the extremal solutions tend to the same (up to a positive scaling factor) antiperiodic solution. An analogue of the Perron-Frobenius theorem for corresponding linear inclusions is obtained. A description of the set of extremal points of the set of extremal norms of linear inclusion is provided