Suboptimal Control of Linear Time-Delay Systems

Mohanty, A.K.; Chhotaray, R.K.

doi:10.1080/03772063.1979.11451825

Cited by 1 publication

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“…This traditional manner of using Pad! e e approximations for time-delay systems has been used extensively; see [25][26][27][28]. However, it can only be used for small delays and over a finite bandwidth of the system, because the Pad!…”

Section: Introductionmentioning

confidence: 99%

New results for the analysis of linear systems with time‐invariant delays

Zhang

Knospe

Tsiotras

2003

Intl J Robust & Nonlinear

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SUMMARYThis paper presents a comparison system approach for the analysis of stability and H 1 performance of linear time-invariant systems with unknown delays. The comparison system is developed by replacing the delay elements with certain parameter-dependent Pad! e e approximations. It is shown using the special properties of the Pad! e e approximation to eÀs that the value sets of these approximations provide outer and inner coverings for that of each delay element and that the robust stability of the outer covering system is a sufficient condition for the stability of the original time delay system. The inner covering system, in turn, is used to provide an upper bound on the degree of conservatism of the delay margin established by the sufficient condition. This upper bound is dependent only upon the Pad! e e approximation order and may be made arbitrarily small. In the single delay case, the delay margin can be calculated explicitly without incurring any additional conservatism. In the general case, this condition can be reduced with some (typically small) conservatism to finite-dimensional LMIs. Finally, this approach is also extended to the analysis of H 1 performance for linear time-delay systems with an exogenous disturbance.

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Section: Introductionmentioning

confidence: 99%