Comparison of two polynomial approaches in performance analysis for periodic piecewise polynomial systems

In this paper, the theory and effectiveness of two polynomial approaches are compared in the analysis of L₂-L_∞ and H_∞ performance for a type of periodic piecewise polynomial systems, where the time-varying subsystems can be characterized in Bernstein polynomials. Using the Bernstein polynomial-based lemma and the existing lemma concerning the negativity/positivity of matrix polynomial functions, sufficient conditions are established in tractable forms aimed at the global asymptotic stability and performance analysis. Four cases of optimization constraints are considered based on the proposed conditions. The performance indices obtained via the four cases are compared through a numerical example, and the lower conservatism achieved by the proposed Bernstein polynomial approach is demonstrated.