The infinite-dimensional dissipation inequality

We study the dissipativity of linear infinite-dimensional systems with respect to a prescribed quadratic supply-rate functional. We characterize this property via an operator inequality that also yields the system’s dissipation rate. We also derive implications for the linear–quadratic optimal control problem on the nonnegative real half-line. 2020 Mathematics Subject Classification 93B28, 37L05, 49N10.