X ( O ) = . X~ (18) and because of the positivity of the integrand in (17) for all x and u it follows [3] that JT+m as T+m if x ( ? ) does not tend to zero as r tends to infinity. Consequently, the class of feasible controls is automatically that which consists of controls which cause x(t)+O as t+co and it is not necessary to impose further restrictions. In contrast in the game situation the integrand of (1) is not positive for all x , u, and c and therefore there may exist sensible strategies which do not force x(r)+O as t+x (see the example in [I]). Consequently. one may restrict the pair u, c to belong to the set UV if one wishes to mimic the linear quadratic control case.A further poinr. noted by M. Pachter. is that if u and c are assumed to be finite energy functions on [0, co). viz.(a typical assumption in differential games), then for (1) to exist as T+m it is necessary, because of the positive definiteness of Q, also that u, c E U V . This is further justification for the definition of the set of feasible strategy pairs U V .
REFERENCES[I] E. F. Mageirou, "Values and strategies for infinite time linear quadratic games," 121 -, "Topics in the study of interconnected systems." Div. Eng. App. Phys., 131 R. W. Brackeit, Finite Dimemiom1 Linear Sysrem.Theorem 2: If A is nearly nonnegative the matrix I + Ar + At2/2! + . . . = eAf > 0 for all t > 0.prooj Again there exists a real number such that A +SI a 0. Thus, ( A +SI)" > 0 for all integers n > 0. Thus, for all t 0, e(A+sl)r > 0;
, -~l I .~( A + s l ) r
Long-path measurements of carbon monoxide in the atmosphere are described. The technique of resonance absorption was used in which the wavelength of radiation from a PbS(0.82)MbSe(0.18) semiconductor diode laser was tuned into coincidence with an absorption line of CO in its fundamental band around 4.7 microm. By employing rapid frequency modulation of the laser emission to overcome atmospheric turbulence effects, it was possible to achieve a minimum detectable concentration of 5 parts per billion over a 0.61-km path. Continuous around-the-clock monitoring was also performed and permitted increases in the ambient CO level due to commuter traffic to be observed.
Additional. quantitative results are presented for the existence of optimal decision rules and stochastic stability for linea r systems with white random parameters with respect to quadratic per fo rmance criteria , by examining a specific version of a multivariable optimization problem.
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