Trentelman, H.L.

Willems, J.C.

English

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, 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, 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

Dissertations of the University of Groningen

Dissipative differential systems and the state space H∞ control problem

https://pure.rug.nl/ws/files/14409076/2000IntJRobNonlinContTrentelman.pdf

Dissipative differential systems and the state space H∞ control problem

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