Delay-dependent H∞H∞ filtering for time-delayed LPV systems

The present paper addresses the parameter-dependent H∞H∞ filter design problem for output estimation in linear parameter varying (LPV) plants that include constant delays in the state. We develop LMI-based delay-dependent conditions to guarantee stability and an induced L2L2 gain bound performance for the filtering error system. An explicit characterization of the filters’ state–space representation is given in terms of the solutions to a convex optimization problem associated with the synthesis conditions. By taking the output estimation error into account as the H∞H∞ criterion, the developed filters are shown to be capable of tracking the desired outputs of the time-delayed parameter varying system in the presence of external disturbances. Two families of filters are examined: memoryless and state-delayed filters. The latter one which involves a delay term in its dynamics has the benefit of reducing the conservatism in the design and improving performance. Illustrative examples are provided to demonstrate the feasibility and advantages of the proposed methodologies for memoryless and state-delayed filter design and to validate the superiority of using the state-delayed configuration compared to the conventional memoryless filters.