Balanced realization and model reduction of singular systems

The problem of balanced realization and model reduction of a singular system of the form E[xdot] = Ax + Bu, where E is a singular matrix, is considered. Using coordinate transformation, which can be computed by performing singular value decomposition of E, we derive our first approach to the balancing of singular systems. The second approach is based on standard form decomposition of singular systems to slow and fast subsystems and performing balanced realization on the decomposed model. In this sense model reduction can be established in two steps: first, by decomposing the singular system and second, by performing balancing transformation on the decomposed subsystems.

[1]  Erik I. Verriest,et al.  On the sensitivity of generalized state-space systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[2]  B. Anderson,et al.  Singular perturbation approximation of balanced systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[3]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[4]  D. Bender.  Lyapunov-like equations and reachability/observabiliy Gramians for descriptor systems , 1987 .

[5]  A. Laub,et al.  Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms , 1987 .

[6]  D. Cobb.  Controllability, observability, and duality in singular systems , 1984 .

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

[8]  John R. Beaumont,et al.  Large-Scale Systems: Modeling and Control , 1983 .

[9]  K. Fernando,et al.  Singular perturbational model reduction in the frequency domain , 1982 .

[10]  L. Silverman,et al.  Model reduction via balanced state space representations , 1982 .

[11]  T. Kailath,et al.  A generalized state-space for singular systems , 1981 .

[12]  R. F. Sincovec,et al.  Solvability, controllability, and observability of continuous descriptor systems , 1981 .

[13]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[14]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .

[15]  Basil G. Mertzios,et al.  Chained aggregation of singular systems , 1989 .