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Robust stabilization of linear systems with norm-bounded time-varying uncertainty. (English) Zbl 0634.93066
For the state model $dx/dt=(A+\Delta A)x(t)+(B+\Delta B)u(t)$, where $[\Delta A,\Delta B]=DF(t)E$, $F\sp T(t)F(t)\le I$, the authors look for stabilizing state feedback based on the solution of a modified algebraic Riccati equation. The approach reminds of the exponential stability approach. Actually, the title should be “Robust state feedback stabilization...”.
Reviewer: A.Vaněček

93D15Stabilization of systems by feedback
93B35Sensitivity (robustness) of control systems
93C05Linear control systems
15A24Matrix equations and identities
93C35Multivariable systems, multidimensional control systems
34D10Stability perturbations of ODE
Full Text: DOI
[1] Barmish, B. R.: Stabilization of uncertain systems via linear control. IEEE trans. Automat. control. 28, No. 8, 848 (1983) · Zbl 0554.93054
[2] Barmish, B. R.: Necessary and sufficient conditions for quadratic stabilizability of uncertain linear systems. J. optim. Theory appl. 46, 399 (1985) · Zbl 0549.93045
[3] Noldus, E.: Design of robust state feedback laws. Internat. J. Control 35, 399 (1982) · Zbl 0491.93050
[4] Petersen, I. R.: A stabilization algorithm for a class of uncertain linear systems. Systems control lett. 8, 351 (1987) · Zbl 0618.93056
[5] Petersen, I. R.: Stabilization of an uncertain linear system in which uncertain parameters enter into the input matrix. (1987) · Zbl 0667.93087
[6] Petersen, I. R.; Hollot, C. V.: A Riccati equation appraoch to the stabilization of uncertain linear systems. Automatica 22, 397 (1986) · Zbl 0602.93055
[7] Petersen, I. R.: Quadratic stabilizability of uncertain linear systems: existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control. IEEE trans. Automat. control 30, 291 (1985) · Zbl 0555.93051
[8] Tannenbaum, A. R.; Khargonekar, P. P.: On weak pole placement of linear systems depending on parameters. Proceedings of the MTNS-83 international symposium, 829 (1983) · Zbl 0539.93039
[9] Zhou, K.; Khargonekar, P. P.: Stabilization of uncertain systems via linear feedback control. (1987)