13 - Related extensions to system well-posedness and internal stability

Abstract

This chapter is concerned with two key notions, i.e., well-posedness and internal stability, which are closely related to control system designs, such as H∞ control and H2 control. By looking into the standard H∞ control scheme in detail, we have presented certain generalizations to the classical concepts of well-posedness and internal stability, which are termed as externally internal well-posedness and externally internal stability. The main significance of these generalizations lies in that the issue of well-posedness can be unifiedly clarified from a general setting, the input-output stability of the closed-loop system can be characterized in terms of the generalized input-output transfer functions. Such generalizations also throw a new light on the impact of the input signal information on system control design.