Robust Multi-Objective Control for Real Uncertainties Via Parameter-Dependent Lyapunov Functions

Abstract The problem of robust mixed H ∞ / H 2 control is addressed in this paper. The considered control law is static state-feedback. The studied uncertain systems are Linear Time Invariant (LTI) and are subject to parametric uncertainty. They are modelled such that the state-space representation of the system belongs to a polytope of matrices. The main contribution is to revisit the Lyapunov Shaping paradigm deriving sufficient LMI -based conditions for various mixed H 2 / H ∞ synthesis problems via the use of parameter-dependent Lyapunov functions. This allows to drastically reduce the conservatism of existing methods.

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