Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability

G. C. Konstantopoulos, Q. C. Zhong, B. Ren, M. Krstic

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

A fundamental problem in control systems theory is that stability is not always guaranteed for a closed-loop system even if the plant is open-loop stable. With the only knowledge of the input-to-state (practical) stability (ISpS) of the plant, in this note, a bounded integral controller (BIC) is proposed which generates a bounded control output independently from the plant parameters and states and guarantees closed-loop system stability in the sense of boundedness. When a given bound is required for the control output, an analytic selection of the BIC parameters is proposed and its performance is investigated using Lyapunov methods, extending the result for locally ISpS plant systems. Additionally, it is shown that the BIC can replace the traditional integral controller (IC) and guarantee asymptotic stability of the desired equilibrium point under certain conditions, with a guaranteed bound for the solution of the closed-loop system. Simulation results of a dc/dc buck-boost power converter system are provided to compare the BIC with the IC operation.

Original languageEnglish
Article number7450628
Pages (from-to)4196-4202
Number of pages7
JournalIEEE Transactions on Automatic Control
Volume61
Issue number12
DOIs
StatePublished - Dec 2016

Keywords

  • Bounded input
  • input-to-state stability
  • integral control
  • nonlinear systems
  • small-gain theorem

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