Title :
J-spectral factorization for general rational matrices with application in robust estimation
Author :
Zhang, Huanshui ; Xie, Lihua ; Soh, Yeng Chai
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore
Abstract :
J-spectral factorization for general discrete rational matrices is considered in this paper. We propose a simple approach based on the Kalman filtering in Krein space. The main idea is to construct a stochastic state space filtering model in Krein space such that the spectral matrix of the output is equal to the rational matrix to be factorized. The spectral factor is then easily derived by using the generalized Kalman filtering in Krein space, which is similar to the H 2 spectral factorization. Our approach unifies the treatment of the H2 spectral factorization and the J-spectral factorization. The applications of the derived results in H∞ and risk-sensitive estimation for both nonsingular and singular systems are demonstrated
Keywords :
H∞ optimisation; Kalman filters; estimation theory; filtering theory; matrix decomposition; state-space methods; stochastic processes; H∞ estimation; H2 optimization; H2 spectral factorization; J-spectral factorization; Krein space; discrete rational matrices; generalized Kalman filtering; nonsingular systems; rational matrix; risk-sensitive estimation; robust estimation; singular systems; spectral matrix; stochastic state space filtering model; Closed-form solution; Filtering; Game theory; Kalman filters; Polynomials; Riccati equations; Robustness; Space technology; State-space methods; Stochastic processes;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.980185
