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Zbl 1070.93039
Park, J.H.
Delay-dependent criterion for guaranteed cost control of neutral delay systems.
(English)
[J] J. Optimization Theory Appl. 124, No. 2, 491-502 (2005). ISSN 0022-3239; ISSN 1573-2878/e

The author considers a system described by a neutral functional differential equation $$\dot{x}(t)-C\dot{x}(t-\tau) = A_0x(t) + A_1x(t-h) + Bu(t)$$ with $(A_0+A_1,B)$ a controllable pair. To this system he associates the quadratic cost function $$J(u,\phi) = \int_0^\infty(x^T(t)Qx(t)+u^T(t)Su(t))dt$$ where $Q>0$, $S>0$ and $\phi\in C^1$ is the initial condition. The paper aims to find a control law $u(t) = -B^TPx(t)$ such that the resulting closed-loop system is exponentially stable with guaranteed quadratic cost $J\leq J^*$, 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.
MSC 2000:
*93D15 Stabilization of systems by feedback
34K40 Neutral equations
93C23 Systems governed by functional-differential equations
93D30 Scalar and vector Lyapunov functions
15A39 Linear inequalities

Keywords: neutral delay equation; guaranteed cost control; Lyapunov method; Linear Matrix Inequalities

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