Extensions to system wellposedness and internal stability

This paper presents certain generalisations to the classical concepts of wellposedness and internal stability. Input consistency and output uniqueness of the closed-loop system in the standard control feedback configurations are discussed. Based on this, a number of notions are introduced such as fully internal wellposedness, externally internal wellposedness, and externally internal stability, which characterize the rich input-output and stability features of general control systems in a general setting. The natural links between externally internal wellposedness and wellposedness, externally internal stability and internal stability are explored. The approach also leads to a generalization to the linear fractional transformation. Finally based on these notions an extended H∞ control problem is defined in a general setting. Key Words—H∞ control, ill-posed control system, externally internal wellposedness, externally internal stability, generalized linear fractional transformation. Corresponding Author: Telephone: Telefax: E-mail: Dr. A. C. Pugh Department of Mathematical Sciences Loughborough University Leicestershire, LE11 3TU, UK +44 (0)1509 223190 +44 (0)1509 223969 [email protected]