H  control of system with I/O delay: a review of some problem-oriented methods

Abstract

Systems with input or output delays form the simplest, and yet one of the most widely applied classes of distributed parameter models. This is a review of some problem-oriented H∞ methods for that class, with an emphasis on computational simplicity. Reviewed methods include operator interpolation, game-theoretic state-space treatments in the time domain, a J-spectral factorization approach, and methods exploiting various ideas from sampled-data theory. Some interesting properties of the (sub)optimal solutions are discussed as well.

H/sup /spl infin// control of systems with multiple I/O delays via decomposition to adobe problems

“…1 with the generalized plant as in (1) satisfying -and the delays and as in (2). Determine whether there exists a proper so that internally stabilizes the system and guarantees that This problem is a nontrivial generalization of the single-delay problem extensively studied in the control literature for the last two decades [4].…”

“…Let and be the stabilizing solutions to the standard Riccati equations; (well defined by the solvability assumption); let and be the gains associated with the state-feedback problem and and the corresponding filtering gains; let and be the (stable) "closed-loop" matrices associated with state-feedback and filtering, respectively. Introduce also the following transfer matrix: (4) where and is a nonsingular matrix obtained by the -factorization of a matrix constructed from the feedthrough term of . It can be shown [14] that so that is bistable.…”

“…Optimal control of time-delay systems has been an active research area since the late 1960s, first in the (LQG) [1], [2] and then in the [3], [4] settings.…”

“…These approaches, however, result in rather abstract results (i.e., in terms of operator Riccati equations), from which it may not be clear what the structures of solvability conditions and controllers are and how (if) they can be computed and implemented. This motivated researchers to seek for more problem-oriented approaches that exploit the special structure of the delay operator; see the review paper [4] and the references therein.…”

Control of friction oscillator by Lyapunov redesign based on delayed state feedback

“…A brief overview of some control approaches was also provided. Many papers have considered only the constant delay case without the nonlinear perturbation [5][6][7]. In fact, time delays are often time-varying or even random.…”