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Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays. (English) Zbl 1170.34054
Linear continuous-time control systems with variable coefficients and variable point delay in the state variables are considered. It is generally assumed that the system matrices are known with some uncertainties. Using Lyapunov functionals and linear matrix inequality, sufficient conditions for feedback stabilizability are formulated and proved. Simple numerical examples, which illustrate theoretical considerations are presented. Moreover, many remarks and comments on stabilization problems for delayed control systems are given. The relationships to the results existing in the literature are mentioned and discussed. Finally, it should be pointed out, that similar stabilization problems have been recently considered in the papers [J. H. Park and O. Kwon, Appl. Math. Comput. 162, No. 2, 627–637 (2005; Zbl 1077.34075)] and [P. G. Park and J. W. Ko, Stability and robust stability for systems with a time-varying delay. Automatica 43, No. 10, 1855–1858 (2007; Zbl 1120.93043)].
##### MSC:
 34K35 Functional-differential equations connected with control problems 93C05 Linear control systems 93C23 Systems governed by functional-differential equations 93D09 Robust stability of control systems 93D15 Stabilization of systems by feedback 34K06 Linear functional-differential equations
##### Software:
LMI toolbox; LMI Control Toolbox
##### References:
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