论文信息 - Upper and lower bounds for approximation in the gap metric

Upper and lower bounds for approximation in the gap metric

Upper and lower bounds for the closest approximant of degree k<n in the gap metric to a plant of degree n are obtained. The bounds are expressed in terms of the singular values of two Hankel operators defined in terms of the symbol of the graph of the plant. The question of robust stability and performance of feedback systems is examined in the context of approximation of plant and controller in the gap metric.

Tryphon T. Georgiou | Malcolm C. Smith

[1] D. Meyer. A Fractional Approach to Model Reduction , 1988, 1988 American Control Conference.

[2] B. Francis,et al. A Course in H Control Theory , 1987 .

[3] Keith Glover,et al. A tutorial on Hankel-norm approximation , 1989 .

[4] Brian D. O. Anderson,et al. Unstable rational function approximation , 1987 .

[5] Mathukumalli Vidyasagar,et al. Some simplifications of the graphical Nyquist criterion , 1988 .

[6] Edward J. Davison,et al. Feedback stability under simultaneous gap metric uncertainties in plant and controller , 1992 .

[7] B. Anderson,et al. Controller reduction via stable factorization and balancing , 1986 .

[8] I. M. Glazman,et al. Theory of linear operators in Hilbert space , 1961 .

[9] Mathukumalli Vidyasagar. Normalised coprime factorizations for nonstrictly proper systems , 1988 .

[10] Tosio Kato. Perturbation theory for linear operators , 1966 .

[11] T. Georgiou,et al. Optimal robustness in the gap metric , 1990 .

[12] Duncan McFarlane,et al. Reduced-order controller design using coprime factor model reduction , 1990 .

[13] Tryphon T. Georgiou,et al. On the computation of the gap metric , 1988 .

[14] K. Glover. All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .