zbMATH — the first resource for mathematics

Eigenstructure assignment-based robust stability conditions for uncertain systems with multiple time-varying delays. (English) Zbl 0886.93049
This paper discusses robust stability of the following uncertain linear time-invariant multi-input, multi-output dynamical system with multiple time-varying delays, \[ \begin{aligned} {dx(t) \over dt} & =\bigl[A+ \Delta A(t) \bigr] x(t)+ \sum^r_{\mu=1} \bigl[E_\mu + \Delta E_\mu (t) \bigr] x \bigl(t-h_\mu (t)\bigr) +\bigl[B +\Delta B(t) \bigr] u(t), \\ y(t) & = \bigl[C+ \Delta C(t) \bigr]x(t). \end{aligned} \] Based on the fact that the dynamic response of a multivariable control system can be modified by means of eigenstructure assignment, a method is presented whereby a new sufficient condition for robust stability is derived.

93D09 Robust stability
34K35 Control problems for functional-differential equations
93B55 Pole and zero placement problems
Full Text: DOI
[1] Andry, A.N.; Shapiro, E.Y.; Chung, J.C., Eignestructure assignment for linear systems, IEEE trans. aerospace electron, syst., AES-19, 711-729, (1983)
[2] Chou, J.H.; Horng, I.R.; Chen, B.S., Dynamical feedback compensator for uncertain time-delay systems containing saturating actuator, Int. J. control, 49, 961-968, (1989) · Zbl 0674.93049
[3] Fletcher, L.R.; Kautsky, J.; Kolka, G.K.G.; Nichols, N.K., Some necessary and sufficient conditions for eigenstructure assignment, Int. J. control, 42, 1457-1468, (1985) · Zbl 0592.93023
[4] Kolmanovskii, V.B.; Nosov, V.R., ()
[5] Manu, M.Z.; Mohammad, J., ()
[6] Ogata, K., ()
[7] Srinathkumar, S., Eigenvalue/eigenvector assignment using output feedback, IEEE trans. autom. control, AC-23, 79-81, (1978) · Zbl 0369.93016
[8] Stoer, J.; Witzgall, C., Transformations by diagonal matrices in a normed space, Numer. math., 4, 158-171, (1962) · Zbl 0117.11101
[9] Su, T.J.; Fong, I.K.; Kuo, T.S.; Sun, Y.Y., Robust stability for linear time-delay systems with linear parameter perturbation, Int. J. syst. sci., 19, 2123-2129, (1988) · Zbl 0653.93046
[10] Wang, S.S.; Lin, T.P., Robust stabilization of uncertain time-delay systems with sampled feedback, Int. J. syst. sci., 19, 399-404, (1988) · Zbl 0639.93049
[11] Weinmann, A., ()
[12] Wu, H.S.; Mizukami, K., Robust stabilization of uncertain linear dynamical systems with time varying delay, J. optim. theory applic., 82, 593-606, (1994) · Zbl 0816.93074
[13] Wu, H.S.; Willgoss, R.A.; Mizukami, K., Robust stabilization for a class of uncertain dynamical systems with time-delay, J. optim. theory applic., 82, 361-378, (1994) · Zbl 0804.93043
[14] Yu, W.; Sobel, K.M.; Shaprio, E.Y., A time domain approach to the robustness of time delay systems, (), 3726-3727
[15] Yu, W.; Piou, J.E.; Sobel, K.M., Robust eigenstructure assignment for the extended medium range air-to-air missile, Automatica, 29, 889-898, (1993) · Zbl 0800.93277
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.