An LMI-based parametrization of all H/sub /spl infin// controllers with applications

The continuous- and discrete-time H/sub /spl infin// control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H/sub /spl infin//-suboptimal controllers, including reduced-order controllers. The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMI's. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H/sub /spl infin// controllers and bear important connections with the controller order and the closed-loop Lyapunov functions. Thanks to such connections, the LMI-based characterization of H/sub /spl infin// controllers opens new perspectives for the refinement of H/sub /spl infin// design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.<
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