A NEW INTEGRAL INEQUALITY APPROACH TO DELAY‐DEPENDENT ROBUST H ∞ CONTROL

A design method for the robust H ∞ control of an uncertain linear system with a time‐varying state delay is proposed. First, an integral inequality that we recently obtained is employed to establish a new delay‐dependent bounded real lemma for a system with a time‐varying delay. The lemma uses neither a model transformation nor a bounding technique for cross terms. Then, the lemma is used in combination with a matrix decomposition method to derive delay‐dependent conditions for the existence of robust H ∞ control based on linear matrix inequalities. Finally, some numerical examples are given to demonstrate the validity of the method.