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Delay-dependent criterion for guaranteed cost control of neutral delay systems. (English) Zbl 1070.93039

The author considers a system described by a neutral functional differential equation

x ˙(t)-Cx ˙(t-τ)=A 0 x(t)+A 1 x(t-h)+Bu(t)

with (A 0 +A 1 ,B) a controllable pair. To this system he associates the quadratic cost function

J(u,φ)= 0 (x T (t)Qx(t)+u T (t)Su(t))dt

where Q>0, S>0 and φC 1 is the initial condition. The paper aims to find a control law u(t)=-B T Px(t) such that the resulting closed-loop system is exponentially stable with guaranteed quadratic cost JJ * , where J * >0 is some number. The paper relies on the choice of a quadratic Lyapunov functional leading finally to some Linear Matrix Inequalities whose feasibility guarantees the problem’s solution.

93D15Stabilization of systems by feedback
34K40Neutral functional-differential equations
93C23Systems governed by functional-differential equations
93D30Scalar and vector Lyapunov functions
15A39Linear inequalities of matrices
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