The paper considers the problem of steering the state of a linear time-varying system to the origin when the control is subject to magnitude constraints. Necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control (satisfying the constraints) which steers the system to the origin from a specified initial epoch (x₀ ,t₀ ). The global result does not require zero to be an interior point of the control set Ω, and the theorem for constrained controllability at (x₀ ,t₀ ) only requires that Ω be compact, not that it contain zero. The results are compared to those available in the literature. Furthermore, numerical aspects of the problem are discussed as is a technique for determining a steering control.
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Schmitendorf et al. (1980) studied this question.