L^infinity-norm computation for linear time-invariant systems depending on parameters

This paper focuses on representing the L∞-norm of finite-dimensional linear time-invariant systems with parameter-dependent coefficients. Previous studies tackled the problem in a non-parametric scenario by simplifying it to finding the maximum y-projection of real solutions (x, y) of a system of the form Sigma = {P=0, dP/dx=0}, where P is in Z[x, y]. To solve this problem, standard computer algebra methods were employed and analyzed. In this paper, we extend our approach to address the parametric case. We aim to represent the ````"maximal" y-projection of real solutions of Sigma as a function of the given parameters.To accomplish this, we utilize cylindrical algebraic decomposition. This method allows us to determine the desired value as a function of the parameters within specific regions of parameter space.