Abstract
Necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with H∞ control are derived using J-spectral factorization theory. The existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled J-spectral factorization problems, with the second factor providing a parametrization of all solutions to the model matching problem. The existence of the J-spectral factors is then shown to be equivalent to the existence of nonnegative definite, stabilizing solutions to two indefinite algebraic Riccati equations, allowing a state-space formula for a linear fractional representation of all controllers to be given. A virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework, and no additional auxiliary Riccati equations are required.
Original language | English |
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Pages (from-to) | 1350-1371 |
Number of pages | 22 |
Journal | SIAM Journal on Control and Optimization |
Volume | 28 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1990 |
Externally published | Yes |
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics