Computation of lower bounds for the induced L₂ norm of LPV systems

Summary Determining the induced L₂ norm of a linear parameter-varying (LPV) system is an integral part of many analysis and robust control design procedures. Most prior work has focused on efficiently computing upper bounds for the induced L₂ norm. The conditions for upper bounds are typically based on scaled small-gain theorems with dynamic multipliers or dissipation inequalities with parameter-dependent Lyapunov functions. This paper presents a complementary algorithm to compute lower bounds for the induced L₂ norm. The proposed approach computes a lower bound on the gain by restricting the parameter trajectory to be a periodic signal. This restriction enables the use of recent results for exact calculation of the L₂ norm for a periodic linear time varying system. The proposed lower bound algorithm also returns a worst-case parameter trajectory for the LPV system that can be further analyzed to provide insight into the system performance.