Showing papers by "Ian R. Petersen published in 1983"
TL;DR: It is shown that a class of ultimate boundedness problems which have been solved to date via nonlinear control, can in point of fact be solved via linear control and some of the so-called matching assumptions can be weakened somewhat.
95 citations
TL;DR: The notion of controllability in dynamical systems with unknown but bounded parameters was introduced in this article, where it is conjectured that the notions of exact control and approximate control are equivalent, and the truth of the conjecture can be readily verified.
3 citations
TL;DR: In this article, Barmish and Schmitendorf introduced the notion of controllability gap, which is the possible existence of systems which satisfy one condition but not the other.
Abstract: This paper is concerned with the problem of steering the state $x(t)$ of the system $\dot x(t) = Ax(t) + Bu(t)$ to a prescribed closed and convex target set X in $R^n $. In addition, admissible control values $u(t)$ are constrained to lie in a prescribed compact set $\Omega $ in $R^m $. In light of the constraint, the term constrained controllability problem is often used to describe the situation above. More precisely, the system is said to be globally$\Omega $-controllable to X if every initial state $x_0 $ can be steered to X in finite time. In a recent paper [B. R. Barmish and W. E. Schmitendorf, IEEE Trans. Automat. Control, AC-25 (1980), pp. 540–547.] two separate conditions were given for global $\Omega $-controllability to X. The first of these conditions was a necessary condition and the second of these conditions was a sufficient condition. This led to the possibility of a so-called controllability gap; that is, the possible existence of systems which satisfy one condition but not the other.In t...
1 citations