2020/08/26 by Hongyinping Feng, Xiao-Hui Wu, Feng, Hongyinping +5
Computer Science · Engineering · Mathematics · Physics and Astronomy · #47A62 #93B52 #93C05 #Advanced Mathematical Modeling in Engineering #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC #msc:47A62 #msc:93B52 #msc:93C05
paper · pdf · doi:10.48550/arxiv.2008.11333
27 pages, 5 figures, this is the first part of the series works: dynamics compensation for linear systems
arxiv created 2020/08/26 · openalex publication_date 2020/08/26 · arxiv updated 2020/08/27 · openalex created_date 2020/09/01 · openalex updated_date 2026/07/28
This is the first part of four series papers, aiming at the problem of actuator dynamics compensation for linear systems. We consider the stabilization of a type of cascade abstract linear systems which model the actuator dynamics compensation for linear systems where both the control plant and its actuator dynamics can be infinite-dimensional. We develop a systematic way to stabilize the cascade systems by a full state feedback. Both the well-posedness and the exponential stability of the resulting closed-loop system are established in the abstract framework. A sufficient condition of the existence of compensator for ordinary differential equation (ODE) with partial differential equation (PDE) actuator dynamics is obtained. The feedback design is based on a novelly constructed upper-block-triangle transform and the Lyapunov function design is not needed in the stability analysis. As applications, an ODE with input delay and an unstable heat equation with ODE actuator dynamics are investigated to validate the theoretical results. The numerical simulations for the unstable heat system are carried out to validate the proposed approach visually.