have negative real parts if the condition (24) is satisfied, and at least one root of Eq. (70) has a positive real part when the inequality (26) is satisfied. For the case of the Earth-pointing satellite, the effect of the postulated friction is thus simply to convert marginal stability into asymptotic stability. As for the case of the rotating satellite, the relationship between the stability of the solution q = 0 of Eq. (71) and the parameters g, h, and d has been shown by V. G. Kotowski 5 to be such that, for d > 0, Fig. 6 is to be replaced with Fig. 8, in which the unshaded region once again corresponds to instability, and the shaded region is now associated with asymptotic stability. Thus it may be surmised that friction effects will be at worst, innocuous, and at best, helpful.The problem considered is the following? given a linear dynamic system of order n, find the best model of order m, in < ra, with which to derive a suboptimal control for the given system. The optimization problem covered is the infinite time, linear, output regulator problem with quadratic cost. The system and model outputs are characterized as elements of an appropriate Hilbert space, and the model output is constrained to be a projection of the system output. In this manner, the optimal model initial condition is expressed as a linear function of the system initial condition, and an-algebraic expression is found for the modeling error which is minimized numerically. An example is presented wherein the pitch plane dynamics of a flexible-bodied rocket vehicle are modeled.
