Conference Paper

Delay-dependent robust stabilization for uncertain time-delay systems with saturating actuators-LMI approach

Dept. of Electron. Eng., Nat. Kaohsiung Univ. of Appl. Sci., Taiwan
DOI: 10.1109/ACC.2002.1025311 Conference: American Control Conference, 2002. Proceedings of the 2002, Volume: 4
Source: IEEE Xplore

ABSTRACT This paper provides new stabilization criteria for a class of uncertain linear time-delay systems with saturating actuators for time-varying delays. Based on Lyapunov-Krasovskii functionals combined with LMI techniques, simple and improved delay-dependent robust stability criteria, which are given in terms of quadratic forms of state and LMI, are derived. The proposed results are applicable to robust control design.

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    ABSTRACT: This paper deals with stabilization criteria for a class of time-varying delay system with saturating actuator. Based on the Lyapunov-Krasovskii functional combining with linear matrix inequality (LMI) techniques and Leibniz-Newton formula, delay-dependent stabilization criteria are derived using a state feedback controller. We also consider as efficient convex optimization algorithms to the time-varying delay system with saturating actuator case: the maximal bound on the time delay, such that the prescribed level of operation range and imposed exponential stability requirements are still preserved. The value of the time-delay as well as its rate of change are taken into account in the design method presented and further permit to reduce the conservativeness of the approach. The results have been illustrated by given numerical examples. These results are shown to be less conservative than those reported in the literature.
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    ABSTRACT: This paper discusses the problems of the delay-dependent robust stability and stabilization for a class of linear time-delay uncertain systems with saturating actuators. Some new delay-dependent stability criteria are derived by taking the relationships between the terms in the Leibniz–Newton formula into account. The stability conditions are formulated as linear matrix inequalities that can be easily solved by various convex optimization algorithms or computing software. Moreover, the stability criteria are extended to the design of a stabilizing state feedback controller. Numerical examples demonstrate that these criteria are effective and are an improvement on previous ones.
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    ABSTRACT: This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.
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