Periodic hamiltonians, periodic Riccati equation and forced nonlinear oscillations

The paper aims to apply linear quadratic theory of periodic sytems (due to Yakubovich) to the case of existence. uniqueness and stability of forced nonlinear oscillations bringing together periodic Hamiltonians and periodic Riccati equations with nonlinear systems with periodic coefficients having a periodic or almost periodic forcing term. This allows obtaining sufficient conditions for the existence of forced nonlinear periodic or almost periodic oscillations expressed in terms of an associated periodic linear Hamiltonian. These conditions might be checked numerically via the established methods for periodic systems.