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Several algorithms are presented for the J-spectral factorization of a para-Hermitian polynomial matrix. The four algorithms that are discussed are based on diagonalization, successive factor extraction, interpolation, and the solution of an algebraic Riccati equation, respectively. The paper includes a special algorithm for the factorization of unimodular para-Hermitian polynomial matrices and deals with canonical, noncanonical, and nearly noncanonical factorizations. >

Mixed sensitivity design of a linear multivariable control system amounts toshaping its sensitivity functions to achieve the design targets of closed-loop system performance and robustness. Both H∞ and H2 optimization may be used to this end. Various tools are available, in particular low and high frequency shaping, and partial pole assignment. The paper describes a technique to help placing the dominant closed loop poles called disturbance modeling

The mixed sensitivity design method for multivariable linear control systems proposed in the companion paper (Kwakernaak, 2001) is applied to the design of a stability augmentation system for the longitudinal motion of a fighter airplane previously studied by Safonov and Chiang (1988). Both $H_\infty$ and $H_2$ mixed sensitivity design are considered. They lead to quite similar results

This paper presents an algorithm for the spectral factorization of a para-Hermitian polynomial matrix. The algorithm is based on polynomial matrix to state space and vice versa conversions, and avoids elementary polynomial operations in computations; It relies on well-proven methods of numerical linear algebra such as Schur decompositions.

The paper presents a tutorial exposition of H∞-optimal regulation theory, emphasizing the relevance of the mixed sensitivity problem for robust control system design.

The problem of J-spectral factorization of polynomial matrices is studied. Existence and uniqueness are discussed, and the differences from the standard case are pointed out. Two first algorithms are proposed for a numerical solution. The first algorithm, which is based on the generalized symmetric factor extraction, features simplicity and is easy to implement via MATLAB. The second algorithm, which is based on diagonalization, applies to a more general class of matrices (including those with zeros on the imaginary axis)