Semigroup Theory With Applications to Systems and Control

Part 1 Basic properties of semigroups: uniformly continuous semigroups strongly continuous semigroups some elemtary examples. Part 2 Generation theorems for semigroups: contraction or dissipative semigroups general CO-semigroups adjoint semigroups integrated semigroups examples. Part 3 Semigroups with special properties: CO-groups differentiable and analytic semigroups fractional powers of closed operators compact semigroups. Part 4 Perturbation theory of semigroups: bounded perturbation of general CO-semigroups relatively bounded perturbation of analytic semigroups relatively bounded perturbation of dissipative semigroups Trotter-Kato approximation theory of semigroups. Part 5 Differential equations on Banach space: linear evolution equations semilinear and quasilinear evolution equations integrated semigroups and evolution equations. Part 6 Stochastic differential equations on Banach space: stochastic integrals linear stochastic evolution equations nonlinear stochastic evolution equations. Part 7 Applications to systems and control: stability controllability and stabilizability stability of measures system identification optimal control linear filtering and partially observed controls optimal control of nonlinear stochastic systems.