Abstract
In this paper, we solve guaranteed level-γ ℋ ∞ control problems in uncertain linear systems. In time-varying systems, we provide a time-varying nonlinear differential equation for these problems, which can be solved via differential equation solvers. In time invariant systems, we present linear matrix inequalities (LMIs), which allow us to overcome the limitations of the existing algebraic Riccati equation (ARE) formulations, where one can hardly find their solutions. Since LMI problems are always convex, one can solve them via convex optimization techniques, such as interior-point methods, and can easily solve them even if additional constraints are considered. As a result, we directly handle the optimal guaranteed-level ℋ ∞ control problem as well as a guaranteed level-γ ℋ ∞ control problem with the maximal stability margin. Finally, we present size-reduced LMIs.
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