Stability and robustness of a linear abstract system

Concepts of the stability and structural stability (robustness) of closed-loop systems are fundamental in control theory. We outline a fragment of linear abstract systems theory, where the above-mentioned concepts are defined. For time-invariant systems, frequency methods with the Fourier transform are widely used. For abstract systems defined in a Hilbert resolution space, these concepts are formulated in terms of transfer operators of closed-loop control systems. The generally accepted concepts are exemplified by model control systems, with emphasis on peculiarities of systems, wherein loss of the stability under small changes of parameters is a possibility. As an example the problem of synthesis of a universal robust controller in the class of polyharmonic disturbances with a finite frequency spectrum is discussed