Robust performance bounds for scalar output of linear system with structured uncertainty

In the present paper, robust stability and robust performance bounds for the scalar output of discrete-time linear systems with structured uncertainty are studied. The additive disturbance is assumed to be bounded and perturbations are described by linear time varying causal operators. The least upper bound for the worst case steady-state maximal amplitude of the scalar output of the system is derived for classes of finite memory and fading-memory perturbations. This robust performance bound is shown to be non-conservative for a class of bounded memory perturbations. The perturbations with exponentially decreasing impulse response are also considered. The last two classes of perturbations make it possible to estimate unknown parameters of the nominal system and the norms of perturbations in closed loop. The results obtained are applied to discrete-time SISO plant with stabilizing linear controller feedback.