Abstract :
First, the harmonic Lyapunov equations claimed on the Hilbert space I2 are restricted to the Banach space I1 for asymptotic stability of finite-dimensional linear continuous-time periodic (FDLCP) systems. Second, solutions to the harmonic Lyapunov equations are scrutinised. Third, the harmonic Lyapunov equations are connected with periodic matrix differential (PMD) Lyapunov equations. The connection sheds new light on periodic solutions to the PMD Lyapunov equations. Fourth, the trace formula of the H2 norm for FDLCP systems is shaped with periodic solutions to the PMD Lyapunov equations. Finally, an algorithm for computing periodic solutions to the PMD Lyapunov equations is proposed, which involves only solutions to algebraic Lyapunov equations. There are numerical examples to illustrate the results.
Keywords :
Banach spaces; Hilbert spaces; Lyapunov methods; asymptotic stability; continuous time systems; differential equations; linear systems; multidimensional systems; time-varying systems; Banach space; Hilbert space; asymptotic stability; finite-dimensional linear continuous-time periodic systems; harmonic Lyapunov equations; periodic matrix differential Lyapunov equations;
