Rate-Dependent Mixed H2/H∞ Filtering for Time Varying State Delayed LPV Systems

The paper addresses the design of parameter-dependent mixed H²/H^∞ filters for output estimation of an LPV plant that includes time-varying delay. It is assumed that the state-space data depend continuously on parameters whose trajectories are not known a priori but can be measured in real-time. We investigate the required conditions to guarantee asymptotic stability, H² and H^∞ requirements in terms of linear matrix inequalities (LMIs). Our synthesis conditions, that provide mixed H²/H^∞ filters, are dependent linearly on the rate of change of the delay. We take the estimation error into account as the performance index and design the filters to minimize the output energy subject to a bound on the Lscr²-gain from noise to estimation error. The designed filters are shown to have the capability of tracking the desired outputs of the plant in the presence of external disturbances and time varying delays. We examine two classes of filters, one that is memoryless and another one that has memory in the filter dynamics. It is shown that the time-delayed filter results in reduced conservatism and improved performance. Illustrative examples are used to verify the design methodology and to demonstrate the superiority of using the proposed delayed configuration compared to the memoryless scheme