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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 $$\align E\dot x(t) & =\sum^2_{i=0} A_ix(t-h_i)+ \int^0_{-d}A_dx(t+s) ds+B_1w(t)\\ x(t) & = 0,\ t\le 0\\ z(t) & =\text{col} \bigl\{C_0x(t),C_1x(t-h_1), C_2x(t-h_2)\bigr\} \endalign$$ 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
93C23Systems governed by functional-differential equations
34A09Implicit equations, differential-algebraic equations
15A39Linear inequalities of matrices
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References:
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