The stabilization of single input uncertain linear systems via linear control
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This paper investigates the problem of stabilizing a single input uncertain linear system using linear state feedback control. The uncertain system is described by a linear state equation which contains uncertain parameters which are unknown but bounded. A quadratic Lyapunov function is used to establish the stability of the closed loop system.
A number of papers have appeared in recent years in which the desired stabilization of the system is achieved using nonlinear state feedback control. The main result of this paper demonstrates that for a class of single input uncertain linear systems, linear state feedback control can equally well be used to achieve this stabilization. That is, we describe a class of single input uncertain linear systems which have the following property: If the system can be stabilized using nonlinear state feedback control, then it can also be stabilized using linear state feedback control.
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