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Robust $${\mathcal H}_{\infty}$$ control of linear neutral systems. (English) Zbl 0988.93024
This paper investigates the problems of robust stability and robust $${\mathcal H}_\infty$$ control for a class of uncertain neutral systems of the form: $\dot x(t)- D\dot x(t-\tau) =(A+\Delta A)x(t)+ (A_d+\Delta A_d) x(t-\tau) +\bigl[B+ \Delta B(t)\bigr] u(t)$ $x(t_0+ \eta) =\varphi(\eta), \quad \forall\;\eta \in[- \tau,0],$ where $$u(t)\in \mathbb{R}^p$$ is the control input, $$A\in \mathbb{R}^{n\times n}$$ and $$A_d\in \mathbb{R}^{n \times n}$$, $$B\in \mathbb{R}^{n\times p}$$ are known real constant matrices, $$\tau>0$$ is an unknown constant delay and $$\Delta A\in \mathbb{R}^{n\times n}$$ $$\Delta A_d\in \mathbb{R}^{n \times n}$$ are matrices of uncertain parameters, $$\Delta B(t)$$ represents time-varying parametric uncertainties.
The class describes linear state models with norm-bounded uncertain system parameters and unknown constant state delay. First, a sufficient condition for robust stability independent of the delay is developed. Then, the author provides a sufficient condition that guarantees an $${\mathcal H}_\infty$$-norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown state delay. In both problems the results are expressed in the form of linear matrix inequalities.

##### MSC:
 93B36 $$H^\infty$$-control 93C23 Control/observation systems governed by functional-differential equations 93D09 Robust stability
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##### References:
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