Infinite-Time Reachability of State-Space Regions by Using Feedback Control

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200 Scopus citations


In this paper we consider some aspects of the problem of feedback control of a time-invariant uncertain system subject to state constraints over an infinite-time interval. The central question that we investigate is under what conditions can the state of the uncertain system be forced to stay in a specified region of the state space for all times by using feedback control. At the same time we study the behavior of the region of n-step reachability as n tends to infinity. It is shown that in general this region may exhibit instability as we pass to the limit, and that under a compactness assumption this region converges to a steady state. A special case involving a linear finite-dimensional system is examined in more detail. It is shown that there exist ellipsoidal regions in state space where the state can be confined by making use of a linear time-invariant control law, provided that the system is stabilizable. Such control laws can be calculated efficiently through the solution of a recursive matrix equation of the Riccati type.

Original languageEnglish (US)
Pages (from-to)604-613
Number of pages10
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - Oct 1972
Externally publishedYes

ASJC Scopus subject areas

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


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