A new LMI approach to analysis of linear systems depending on scheduling parameter in polynomial forms

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 L² 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 L² 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 L² gain analysis for a gasturbine engine model which is described as a linear system with a scheduling parameter in polynomial form of two degree.