Complete solution of the 4-block H∞ control problem with infinite and finite jω-axis zeros
✍ Scribed by Xin Xin; Brian D. O. Anderson; Tsutomu Mita
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 174 KB
- Volume
- 10
- Category
- Article
- ISSN
- 1049-8923
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✦ Synopsis
This paper discusses the 4-block H control problem with in"nite and "nite j -axis invariant zeros in the state-space realizations of the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output, where these realizations are induced from a stabilizable and detectable realization of the generalized plant. This paper extends the DGKF approach to the H control problem but permitting in"nite and "nite j -axis invariant zeros by using the eigenstructures related to these zeros. Necessary and su$cient conditions are presented for checking solvability through checking the stabilizing solutions of two reduced-order Riccati equations and examining matrix norm conditions related to the j -axis zeros. The parameterization of all suitable controllers is given in terms of a linear fractional transformation involving a certain "xed transfer function matrix and together with a stable transfer function matrix with gain less than 1 which is free apart from satisfying certain interpolation conditions.