Strong stability of internal system descriptions

The concept of “strong stability” of LTI systems is introduced. This is a stronger notion of stability compared to alternative definitions, which allows the analysis and design of control systems with no overshooting response for arbitrary initial conditions. In this part of the paper strong stability is formally defined and related to various system properties, in particular asymptotic stability, system structure and skewness of eigenframe. State-space transformations under which strong stability is a system invariant are characterised. The results are illustrated by means of numerous examples.