Designing the inverse of an LPTV system using ℋ∞ optimization

This paper investigates the problem of designing the inverse of a linear periodic time varying (LPTV) system. Input and output switching representations of LPTV systems are useful in reducing the problem to that of designing the synthesis filters of the uniform filter bank (UFB) for perfect reconstruction. We use the fact that the cascade connection of the LPTV system and its inverse has to result in a finite delay system. Our design aims at minimizing the worst case error norm. This problem is solved by minimizing the ℋ_∞ norm of the corresponding error system. For the choice of FIR synthesis systems, the problem is modeled as a standard Linear Matrix Inequalities(LMI) problem.