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A differential synthesis technique is developed for multiple input linear feedback systems that allows direct calculation of the set of feedback gains and control interconnects that yield arbitrarily selected flying qualities parameters. This is accomplished by parametrically relating differential gain and interconnect changes to differential changes in flying qualities parameters. The procedure is illustrated by synthesizing a linear feedback control for the linearized lateral dynamics of a lifting-body entry vehicle with unacceptable flying qualities in the unaugmented condition. The differential synthesis method developed in this paper is suitable for digital computer formulation and is easily adapted to systems of high order. B(s) B k c C CĈ i p Ci r Ĉn p Cnr Cy d(s) d k G gradj grad c P grad g P H I I* I, IxzK Nomenclature = differential transition matrix = leading coefficient of the numerator quadratic in the /8 a transfer function = matrix polynomial in s = matrix coefficients of powers of s in B(s) = vector containing the dk and «#& coefficients = input matrix = rolling moment coefficient due to sideslip = damping in roll coefficient = rolling moment coefficient due to yaw rate = aileron rolling moment coefficient = rudder rolling moment coefficient = static directional stability coefficient = yawing moment coefficient due to roll rate = damping in yaw coefficient = aileron yawing moment coefficient = rudder yawing moment coefficient = lateral force coefficient due to sideslip = lateral force coefficient due to rolling velocity = lateral force coefficient due to yawing velocity == lateral force coefficient due to aileron deflection = lateral force coefficient due to rudder deflection = characteristic polynomial of A = coefficients of powers of s in d(s) = vector function of vector g, f(g) = c = control interconnect matrix = vector containing elements of the gain and interconnect matrices = feedback gain matrix = matrix whose element in ith row and jth column is matrix whose element in ith row and jth column is dP>/dc, matrix whose element in ith row and jth column is ap t -/dfcaugmented differential transition matrix commensurable identity matrix rolling moment of inertia yawing moment of inertia product of inertia augmented input matrix . * Aerospace Technologist, Langley Station. Member AIAA. t Aerospace Technologist, Langley Station. m = dimension of u n = dimension of x p = roll rate P(c,q) = algebraic identities between c and q q = vector of flying quality parameters r = yaw rate s = Laplace transform variable u = input control vector u p = input control vector to the augmented system W = weighting matrix x = state vector otijk = coefficient of the (n-k)th power of s in the Xi/Uj transfer function numerator (3 = sideslip angle, deg d a = aileron deflection, deg 5 r = rudder deflection, deg Atfc = commensurable unit vector with 0 in all but kth position w^ = natural frequency of numerator quadratic in the /5 a transfer function o)d = natural frequency of dutch roll mode = bank angle, deg o-=...