Premium
Dissipative differential systems and the state space ℋ︁ ∞ control problem
Author(s) -
Trentelman H. L.,
Willems J. C.
Publication year - 2000
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/1099-1239(200009/10)10:11/12<1039::aid-rnc538>3.0.co;2-5
Subject(s) - dissipative system , state space , state (computer science) , space (punctuation) , control theory (sociology) , differential (mechanical device) , control (management) , mathematics , computer science , classical mechanics , physics , artificial intelligence , thermodynamics , algorithm , statistics , operating system
The purpose of this paper is to apply our very recent results on the synthesis of dissipative linear differential systems to the ‘classical’ state space ℋ ∞ control problem. We first review our general problem set‐up from Willems and Trentelman, IEEE Transactions on Automatic Control , Submitted, where the problem of rendering a given plant dissipative by general interconnection, is reformulated as the problem of finding a suitable dissipative behaviour wedged in between the ‘hidden’ behaviour and the ‘manifest’ behaviour of the plant. We review our main result from Willems and Trentelman, which states that a necessary and sufficient condition for the existence of such behaviour is, that the hidden behaviour and manifest behaviour are dissipative with respect to suitable supply rates, and have storage functions that satisfy a certain coupling condition. We then apply this result to the state‐space ℋ ∞ control problem. We show that our general result in this case reduces to the existence of solutions to certain algebraic Riccati equations, satisfying the well‐known coupling condition. We also derive state‐space formulas for the required controllers. Copyright © 2000 John Wiley and Sons, Ltd.