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This paper proposes a new LMI approach to analysis of linear systems depending on scheduling parameter in polynomial forms: we first propose a method to reduce the parameter dependent LMI condition, which characterizes internal stability and  L  2  gain, to the finite number of LMI conditions by introducing a convex polyhedron which includes a polynomial curve parameterized by scheduling parameter; next we propose a systematic procedure to construct the convex polyhedron. Our approach enable us to analyze  L  2  gain of linear systems with scheduling parameter in polynomial forms through computation of the finite number of LMIs. To show efficacy of our approach, we finally make a numerical experiment of  L  2  gain analysis for a gasturbine engine model which is described as a linear system with a scheduling parameter in polynomial form of two degree.

A New LMI Approach to Analysis of Linear Systems Depending on Scheduling Parameter in Polynomial Forms