A Linear Matrix Inequality Approach to H∞ Control
Abstract¶
The continuous-time and discrete-time H∞ 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∞-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 LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H∞ 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∞ controllers opens new perspectives for the refinement of H∞ design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.
Summary¶
Reformulates continuous- and discrete-time H-infinity control in terms of linear matrix inequalities, replacing traditional indefinite Riccati-equation conditions with convex feasibility problems and controller parametrizations. The LMI viewpoint also exposes controller-order and Lyapunov-function structure, opening practical design routes for robust and reduced-order controllers.
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