Automatica. A Journal of IFAC, the International Federation of Automatic Control (Automatica J. IFAC) (20230101), 153, Paper No 111012, 13~pp. ISSN: 0005-1098 (print).eISSN: 1873-2836.
Subject
65 Numerical analysis -- 65P Numerical problems in dynamical systems 65P10 Hamiltonian systems including symplectic integrators
93 Systems theory; control -- 93C Control systems 93C80 Frequency-response methods
This paper revisits several problems related to frequency-limited and time-limited $\Cal H_2$-optimal model order reduction for linear time-invariant systems, by means of the so-called oblique projection framework (OPF). The discussion verifies and advances some existing theories and algorithms. The main points are: \roster \item"(i)" it is impossible to satisfy all necessary conditions for fixing the local minimizer via OPF; \item"(ii)" equivalence between the interpolation-based conditions and the Gramians-based ones for the local optimum is considered; \item"(iii)" OPF iterative algorithms are developed; and \item"(iv)" model reduction deviation convergence is examined, which reveals that deviation decays as the reduced-model order grows. \endroster \par Benchmark examples are sketched.