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

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.

### 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.)
Full Text: