Robust control in state space

Abstract

We consider the problem of robustness, in particular that of robust stability. Such a problem is amenable to analysis by frequency domain techniques, and also using state space methods. Using some recent state space theory yielding the exact radius of the ball around a nominally stable system within which all additive perturbations retain stability, we show how control action may be implemented to increase the radius of this ball. We present further some material on how destabilizing perturbations may be constructed from solutions of Riccati equations, and how the above mentioned radii may be found with respect to an alternative norm to the one used above. Finally we give some remarks on the use of Lyapunov functions for systems