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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.

93B36 \(H^\infty\)-control
93C23 Control/observation systems governed by functional-differential equations
93D09 Robust stability
Full Text: DOI
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