Time Constant Estimation of Asymptotically Stable Linear System by Lyapunov Function

Keywords: Energy attenuation rate, Initial state response, Lyapunov function, Time constant. Abstract: This paper aims at estimating the time constant of the asymptotically stable control system. The energy varying rate of the system states is defined based on Lyapunov function and its differential function. The minimum energy attenuation rate is defined and solved by the function condition extreme method. The system time constant is estimated to be double of the multiplicative inverse of the minimum energy attenuation rate by taking into account of that the system energy is one order higher than the system state. Application example about a third order control system indicates that the solved time constant is just the response time of the initial states and yet it is irrelevant to the initial states of the system. So this time constant can serve as the estimation value of the response time and this estimated time constant can be used to evaluate the rapidity performance for the asymptotically stable control system.