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7.3 Riccati equations and inequalities in robust control

This section builds on Chapter 6, with the goal of demonstrating that the tools and results of that chapter--in particular, optimality conditions expressed in terms of algebraic Riccati equations--continue to play a central role in the context of more general control problems. The first problem studied here is a special case of the infinite-horizon LQR problem except that the matrix $ Q$ in the cost functional is no longer positive semidefinite, which leads to its interpretation as the problem of characterizing the disturbance-to-output $ \mathcal L_2$ gain. Afterwards, we take a brief look at the $ \mathcal H_\infty $ control problem, which has been an important benchmark problem in robust control theory.


Daniel 2010-12-20