Robust Stability and Robust Stabilization of Uncertain Linear Time-Delay Systems

M.N. Alpaslan Parlakçı (Turkey)


Control systems, time-delay, uncertainty, stability, stabilization, linear matrix inequalities.


In this paper, the problem of robust stability analysis and robust stabilization with memoryless state feedback control for linear systems with time-varying delayed state and norm-bounded time-varying uncertainties are investigated. The proposed method employs Leibniz Newton type model transformation, but unlike existing approaches, it does not involve any additional dynamics. As the additional dynamics induce additional eigenvalues that may move into the right-hand complex s-plane before any of the eigenvalues of the original system does, it causes conservatism in the system. Moreover, quite a few existing methods do apply Leibniz-Newton model transformation without including additional dynamics. However, the matrix inequalities that they obtained are not in the form of linear matrix inequalities. Thus, these matrix inequalities could not be solved by using any convex optimization algorithms. Instead, they could only give suboptimal maximal delay bounds. However, our proposed stability and stabilization criteria depending on both the size of the time delay and its derivative are derived in the form of solvable linear matrix inequalities that can be easily converted into a generalized eigenvalue minimization problem. Numerical examples given for the purpose of comparison with some existing results show that the proposed robust stability and robust stabilization criteria yield less conservative results.

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