Finite-dimensional approximations of unstable infinite-dimensional systems
This paper studies approximation of possibly unstable linear time-invariant infinite-dimensional systems. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. A procedure is developed for constructing a sequence of finite-dimensional approximants, which converges to the given model in the L∞ norm under a mild frequency domain condition. It is noted that the proposed technique uses only the FFT and singular value decomposition algorithms for obtaining the approximations. Numerical examples are included to illustrate the proposed method.
Publication Source (Journal or Book title)
SIAM Journal on Control and Optimization
Gu, G., Khargonekar, P., Lee, E., & Misra, P. (1992). Finite-dimensional approximations of unstable infinite-dimensional systems. SIAM Journal on Control and Optimization, 30 (3), 704-716. https://doi.org/10.1137/0330039