Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals |
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Authors: | Yuanqing Xia Yingmin Jia |
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Affiliation: | The Seventh Research Division, Beijing University of Aeronautics and Astronautics, Beijing 100083, China |
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Abstract: | This paper considers the problem of robust stability and robust stabilization for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. First of all, for robust stability problem, we exploit new matrix inequalities characterization of delay-dependent quadratic stability results, demonstrate that it allows the use of parameter-dependent Lyapunov functionals, and develop control design methods based on linear matrix inequalities (LMIs) for solving the robust control problem. Next, the problem of determining the maximum time-delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. Finally, illustrative examples are given to demonstrate the advantage of these new representations. |
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Keywords: | Time-delay systems Uncertain systems Robust stability Robust stabilization LMI Parameter-dependent Lyapunov functions |
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