This note considers the problem of stabilizing a linear dynamical system (Σ) whose state equation includes a time-varying uncertain parameter vector q(\cdot) . Given the dynamics \dot{x}(t)=A(q(t))x(t)+ B(q(t))u(t) and a bounding set Q for the values q(t) , the objective is to choose a control law u(t)=p(x(t)) guaranteeing uniform asymptotic stability for all admissible variations of q(\cdot) . Our results differ from previous work in one fundamental way; that is, we show that when working with linear controllers, it is possible to dispense with all assumptions on B(\cdot) which have been made by previous authors (e.g., see [1]-[9]). This elimination of hypotheses on B(\cdot) is accomplished roughly as follows: the system (\Sigma) {\underline {\underline \Delta}} (A(q), B(q)) is shown to be equivalent to another system (\Sigma^{+}) {\underline {\underline \Delta}} (A^{+}(q), B^{+}) as far as stabilization is concerned. Since B^{+} is a constant matrix (independent of q ), the desired result is readily obtained.

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