Abstract: Multi-objective robust state-feedback controller synthesis problems for linear discrete-time uncertain systems are addressed. Based on parameter-dependent Lyapunov functions, the Gl₂ and GH₂ norm expressed in terms of LMI (Linear Matrix Inequality) characterizations are further generalized to cope with the robust analysis for convex polytopic uncertain system. Robust state-feedback controller synthesis conditions are also derived for this class of uncertain systems. Using the above results, multi-objective state-feedback controller synthesis procedures which involve the LMI optimization technique are developed and less conservative than the existing one. An illustrative example verified the validity of the approach.

Key words: Gl₂ and GH₂ performance, Multi-objective optimization, Robust controller synthesis, Parameter-dependent Lyapunov functions, Convex polytopic uncertain system

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