Dissipativity for Lur’e distributed parameter control systems

In this work, dissipativity of Lur’e distributed parameter control systems has been addressed. Delay-dependent sufficient conditions for the dissipativity with respect to the infinite-dimensional version of energy supply rate (Q1,S1,R1Q1,S1,R1) characterized exclusively by unbounded   operator Q1Q1 are established in terms of linear operator inequalities (LOIs). Finally, the heat equation illustrates our result.