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\(H _{\infty}\)-control of linear state-delay descriptor systems: An LMI approach. (English) Zbl 1006.93021
The \(H^\infty\) control of the linear state-delay descriptor system \[ \begin{aligned} E\dot x(t) & =\sum^2_{i=0} A_ix(t-h_i)+ \int^0_{-d}A_dx(t+s) ds+B_1w(t)\\ x(t) & = 0,\;t\leq 0\\ z(t) & =\text{col} \bigl\{C_0x(t),C_1x(t-h_1), C_2x(t-h_2)\bigr\} \end{aligned} \] is studied, and a delay-dependent robust controller without impulsive solutions is obtained. The method is based on the standard use of linear matrix inequalities.

MSC:
93B36 \(H^\infty\)-control
93C23 Control/observation systems governed by functional-differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
15A39 Linear inequalities of matrices
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