Destabilization by Output Feedback

In this paper we investigate the robustness of stability of linear systems _ x = Ax resp. x(t + 1) = Ax(t) under complex or real (i) time-varying linear, (ii) nonlinear, (iii) time-varying nonlinear, or (iv) dynamic parameter perturbations of the output feedback type. The class of dynamic perturbations is suuciently wide to account for all kinds of neglected dynamics with nite gain encountered in applications, including perturbation operators with unbounded memory. For each of the above perturbation classes the stability radius of the given system is deened to be the norm of the smallest destabilizing perturbation. If complex perturbations are considered, the four corresponding stability radii turn out to be identical, whereas for real perturbations the stability radii depend on the speciic perturbation class. These results are established for both discrete and continuous time systems. In the diierentiable case a multivariable extension of the Aizerman conjecture is discussed in detail for both real and complex nonlinearities.