Passivity analysis and synthesis for uncertain time-delay systems. (English) Zbl 1014.93038

Mahmoud, Magdi S.; Xie, Lihua

Math. Probl. Eng. 7, No. 5, 455-484 (2001).

The notions of asymptotic and strong stability are generalized to include passivity for a linearized water pollution model of the form \[ \begin{aligned} \dot x(t) & = (A_0+\Delta A) x(t)+ B_0w(t)+ E_0x(t-\tau)+ G_0 u(t),\\ z(t) &= (C_0+\Delta C) x(t)+ D_0w(t).\end{aligned} \] Conditions for the robust stability with passivity are first given in terms of standard LMI’s. Using the \(\mu\)-parameterization technique, the system is expanded to one which does not contain uncertain parameters, which means that the results are technically easier to obtain. Finally, the theory is applied to obtain a stabilizing control by an observer-based control synthesis.

Reviewer: Stephan Paul Banks (Sheffield)

MSC:

93D21	Adaptive or robust stabilization
93C23	Control/observation systems governed by functional-differential equations
93D09	Robust stability
93B51	Design techniques (robust design, computer-aided design, etc.)

Keywords:

delay; robust stabilization; strong stability; passivity; water pollution model; robust stability; \(\mu\)-parameterization technique