Robust delay-dependent H<inf>∞</inf> filtering for a class of LPV state-delayed systems

This paper deals with the robust delay-dependent H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋡</inf> filtering problem for a class of LPV systems with multiple constant time-delays in the state vector. It is shown that, by using the Hamiltonian-Jacoby-Isaac (HJI) function and the polynomially parameter-dependent quadratic functions and a suitable change of variables, the required sufficient conditions with high precision are established in terms of parameter-independent linear matrix inequalities (LMIs) for the existence of the desired H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋡</inf> filters. However, the explicit expression of the robust delay-dependent H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋡</inf> filters is derived to satisfy both asymptotic stability and H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋡</inf> performance. A numerical example is provided to demonstrate the validity of the proposed design approach.