Construction of Continuous and Piecewise Affine Feedback Stabilizers for Nonlinear Systems

Tom R.V. Steentjes (Corresponding author), Mircea Lazar, Alina I. Doban

Research output: Contribution to journalArticleAcademicpeer-review


In this article, two methods for constructing continuous and piecewise affine (CPA) feedback stabilizers for nonlinear systems are presented. First, a construction based on a piecewise affine interpolation of Sontag's “universal” formula is developed. Stability of the corresponding closed-loop system is verified a posteriori by means of a CPA control Lyapunov function and subsequently solving a feasibility problem. Second, we develop a procedure for computing CPA feedback stabilizers via linear programming, which allows for the optimization of a control-oriented criterion in the synthesis procedure. Stability conditions are a priori specified in the linear program, which removes the necessity for a posteriori verification of closed-loop stability. We illustrate the developed methods via two application-inspired examples considering the stabilization of an inverted pendulum and the stabilization of a healthy equilibrium of the hypothalamic-pituitary-adrenal axis.
Original languageEnglish
Article number9222222
Pages (from-to)4059-4068
Number of pages10
JournalIEEE Transactions on Automatic Control
Issue number9
Publication statusPublished - 1 Sept 2021


  • Lyapunov methods
  • Nonlinear systems
  • Stability criteria
  • Closed loop systems
  • Interpolation


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