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Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach. (English) Zbl 0889.93050

This paper considers the problems of robust stability and robust control design for the following uncertain linear systems with delay: \[ \begin{cases} \dot x(t) &=\bigl[A + \Delta A(t)\bigr] x(t)+ [Ad+\Delta Ad] x(t-\tau) \\ & +\bigl[B +\Delta B(t) \bigr] u(t) \\ x(t) &= \varphi(t), \quad t\in [-\tau,0]. \end{cases} \] Some methods are developed based on linear matrix inequalities and depending on the size of the time delay.

MSC:

93D21 Adaptive or robust stabilization
34K20 Stability theory of functional-differential equations
93D09 Robust stability
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