论文信息 - Closed-loop balanced realizations of LTI discrete-time systems

Closed-loop balanced realizations of LTI discrete-time systems

Abstract The problem of closed-loop balancing discrete LTI models is addressed. It is shown that results similar to those known for the continuous case can be extended to the discrete case. A new cross-Riccati equation is introduced which allows the direct balancing of MIMO symmetric discrete systems avoiding the solution of the two traditional Riccati equations for Kalman filtering and LQG control. Moreover, some suitable properties of such a cross-Riccati equation are shown. Finally, a method for obtaining discrete approximated models, based on the introduced equation, which appears to be suitable for approximating LQG controllers, is shown.

Giovanni Muscato | Luigi Fortuna | Giuseppe Nunnari

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

[2] Edmond A. Jonckheere,et al. A new set of invariants for linear systems--Application to reduced order compensator design , 1983 .

[3] L. Silverman,et al. Stochastic balancing and approximation - Stability and minimality , 1983, The 22nd IEEE Conference on Decision and Control.

[4] J. Ramos,et al. A note on a cross Riccatian and related properties for symmetric stochastic realizations , 1987, 26th IEEE Conference on Decision and Control.

[5] Luigi Fortuna,et al. On the solution of a nonlinear matrix equation for MIMO symmetric realizations , 1988 .

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

[7] A. Laub. A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[8] Jan C. Willems,et al. REALIZATION OF SYSTEMS WITH INTERNAL PASSIVITY AND SYMMETRY CONSTRAINTS , 1976 .

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