## A Frequency Domain Approach to the Design and Analysis of Linear Multivariable Systems |

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achieve asymptotically stable Au(s C(sI characteristic polynomial closed loop optimal closed loop poles closed loop transfer companion form companion matrix composite system constraints corollary C7 CS(s decoupled system decoupled via linear decoupling state variable decoupling via input defined design algorithms determined diagonal matrix eigenvalues employed expression feedback design feedback matrix frequency domain Furthermore helicopter IEEE Trans input dynamics Kalman lateral cyclic pitch linear multivariable systems linear optimal control linear state variable loop transfer matrix main rotor collective matrix given matrix of polynomials minimal realization noninteraction nonsingular nonsingular matrix obtain optimal poles optimal system orthogonal matrix output feedback output regulator problem pair A,b particular pole assignment Riccati equation root locus root-square locus rp rp scalar systems Section 5.1 spectral factorization stability STEP structure theorem system Eq system x theorem Tl transfer functions variable feedback vector zero