2020/07/28 by Alexis J. Vallarella, Vallarella, Alexis J., Paula Cardone +3
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2007.14011
openalex publication_date 2020/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Exact discrete-time models of nonlinear systems are difficult or impossible\nto obtain, and hence approximate models may be employed for control design.\nMost existing results provide conditions under which the stability of the\napproximate model in closed-loop carries over to the stability of the (unknown)\nexact model but only in a practical sense, i.e. the trajectories of the\nclosed-loop system are ensured to converge to a bounded region whose size can\nbe made as small as desired by limiting the maximum sampling period. In\naddition, some very stringent conditions exist for the exact model to exhibit\nexactly the same type of asymptotic stability as the approximate model. In this\ncontext, our main contribution consists in providing less stringent conditions\nby considering semiglobal exponential input-to-state stability (SE-ISS), where\nthe inputs can successfully represent state-measurement and actuation errors.\nThese conditions are based on establishing SE-ISS for an adequate approximate\nmodel and are applicable both under uniform and nonuniform sampling. As a\nsecond contribution, we show that explicit Runge-Kutta models satisfy our\nconditions and can hence be employed. An example of control design for\nstabilization based on approximate discrete-time models is also given.\n