Stabilization of time-varying pseudo-Hamiltonian systems

In this note, the problem of stability and stabilization of time-varying pseudo-Hamiltonian control systems is investigated. First, we show a stability result for time-varying pseudo-Hamiltonian dynamic systems. The relationships among the Lyapunov function, storage function and the Hamiltonian function are revealed. Roughly speaking, they are essentially equivalent. Then a new development on the stability of 𝒦 + L systems is reported. Based on this new approach the stabilization problem of time-varying systems is considered. Certain results are parallel to their counterparts in time-invariant systems.