Generalized state scaling and applications to feedback, feedforward, and nontriangular nonlinear systems

P. Krishnamurthy, F. Khorrami

Research output: Contribution to journalArticle


We propose a global high-gain scaling-based state-feedback controller for a general class of nonlinear systems containing uncertain functions of all the states and the control input as long as polynomial bounds on ratios of some uncertain system terms are available. The design is based on a high gain scaling involving appropriate powers of a high gain scaling parameter which is a dynamic signal driven by the state. The design is applicable to both lower triangular (strict-feedback) and upper triangular (feedforward) systems, and also to nontriangular systems as long as a set of linear inequalities involving powers of the polynomial bounds on the ratios of uncertain system terms and scaling orders is solvable. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov inequalities.

Original languageEnglish (US)
Pages (from-to)102-108
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - Jan 1 2007



  • Feedforward systems
  • High gain
  • Nonlinear systems
  • Scaling
  • Strict-feedback systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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