## A method to stabilize linear systems using Eigenvalue gradient informationNational Aeronautics and Space Administration, Scientific and Technical Information Branch, 1985 - Mathematics - 37 pages |

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aiqeuBA augmented system matrix chosen coefficients complex conjugate complex matrix control inputs control-law designer DAST ARW-2 defined denominator polynomial derived design algorithm design variables dP jk drawdown factor dXi dP eigen eigenvalues with respect elements equa exponential function flow chart following equation formance index formed from parti FORTRAN fourth-order control law given in equations History of eigenvalues History of normalized identity matrix initial control law initial values iterations 12 14 iterations Figure Kreisselmeier-Steinhauser KS Kronecker delta Langley Research Center law that stabilizes left eigenvectors matrix formed methods and eigenvalue multi-input multi-output lateral-directional Na+M)x(Na+M NASA normalized eigenvectors normalized performance index Number of iterations numerator polynomial optimization process order control law reduced-order control laws right eigenvectors second application—case second-order control law shown in figure stabilizing control law stable closed-loop system starting point tr jk transfer function matrix type 2 design value of gain variables are shown vector of order yaw rate