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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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