Stability

Abstract

This chapter describes the stability of a linear system from different points of view: bounded-input bounded-output stability (I/O representation, external stability) and the stability of the zero solution of $\dot x = A\left( t \right)x$ (state representation, internal stabil­ity): for the latter case the notions of asymptotic-and exponential-stability are developed. More specific topics conclude the chapter: bounded trajectories and regula­tion, response of a linear stable system to T-periodic inputs, equilibrium solution of a driven T-periodic differential system and slightly nonlinear systems.