Dissipative differential systems and the state space H-infinity control problem

The purpose of this paper is to apply our very recent results on the synthe sis of dissipative linear differential systems to the 'classical' state spa ce H-infinity, control problem. We first review our general problem set-up from Willems and Trentelman, IEEE Transactions on Automatic Control, Submit ted, where the problem of rendering a given plant dissipative by general in terconnection, is reformulated as the problem of finding a suitable dissipa tive behaviour wedged in between the 'hidden' behaviour and the 'manifest' behaviour of the plant. We review our main result from Willems and Trentelm an, which states that a necessary and sufficient condition for the existenc e of such behaviour is, that the hidden behaviour and manifest behaviour ar e dissipative with respect to suitable supply rates, and have storage funct ions that satisfy a certain coupling condition. We then apply this result t o the state-space H-infinity control problem. We show that our general resu lt in this case reduces to the existence of solutions to certain algebraic Riccati equations, satisfying the well-known coupling condition. We also de rive state-space formulas for the required controllers. Copyright (C) 2000 John Wiley and Sons, Ltd.