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Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays

L. Hetel, J. Daafouz, C. Iung
2006 IEEE Transactions on Automatic Control  
values of P (i!1) are 11 = 0:6811 and 12 = 0:0628, and the singular values of P (i! 2 ) are 21 = 0:3063 and 22 = 0:0450. The bounds for the modal cost functions J k are given by Theorem 8 8:1 min K 2S J 1 (K 1 ) 15:0 11:4 min K 2S J 2 (K 2 ) 20:6: P (i! k ). If either the reference or disturbance signal is absent these bounds are tight. It is an open problem whether the gains K ka and K kb are optimal also in the multiple output case, nevertheless they are shown to be good choices. To the
more » ... oices. To the authors' knowledge the main results are new even for finite-dimensional systems. The gains K ka and K kb depend only on the values P (i! k ) of the transfer function at the reference and disturbance signal frequencies ! k . It is also shown that for well-posed regular systems the values P (i! k ) can be determined using input-output measurements from the open-loop plant. Hence, the results are applicable also when no plant model is available. One-dimensional heat equation with Dirichlet boundary control and pointwise measurements was given as an example to demonstrate the solutions. Abstract-We consider continuous time switched systems that are stabilized via a computer. Several factors (sampling, computer computation, communications through a network, etc.) introduce model uncertainties produced by unknown varying feedback delays. These uncertainties can lead to instability when they are not taken into account. Our goal is to construct a switched digital control for continuous time switched systems that is robust to the varying feedback delay problem. The main contribution of this note is to show that the control synthesis problem in the context of unknown time varying delays can be expressed as a problem of stabilizability for uncertain systems with polytopic uncertainties. Index Terms-Linear matrix inequality (LMI), polytopic uncertainties, robustness, switched linear systems, time-varying feedback delays.
doi:10.1109/tac.2006.883030 fatcat:lhbhxknfmjfydjwe443u6gekea