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Abstrucf-Thisnote deals with a special type of asymptotic stability, namely componentwise asymptotic stability with respect to the vector y ( t ) (CWAS y ) of system S: P = Ax + Bu, t 0, mrhere y ( t ) > 0 (component-with the components Ix,(to)l the free response of S satisfies I x ( t ) ( < y ( t ) for each t > to. For y ( t ) A ae-O', t > 0, with (2 > 0 and /3 > 0 (scalar), the CWEAS ( E = exponential) may be defined. S is C W A S y (CWEAS) if and only if q ( r ) &(r), f > 0 (& < 0); A (a;,) and x has the elements a,i and la,,], i f j . These results may be used in order to evaluate in a more detailed manner the dynamical behavior of S as well as to stabilize S componentRise by a suitable linear state feedback.

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