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Finite-time control of linear systems subject to parametric uncertainties and disturbances. (English) Zbl 0983.93060
The authors consider a linear system subject to time-varying parametric uncertainties and to exogenous constant disturbances $$\dot x(t) = A(p)x(t) + B(p)u(t) + G(p)w,$$ where $A(p)\in\Bbb R^{n\times n}$, $B(p)\in\Bbb R^{n\times m}$ and $G(p)\in\Bbb R^{n\times l}$. The concept of finite-time boundedness for the state of a system, when not only given initial conditions but also external constant disturbances are considered, is introduced. The main result provided is a sufficient condition guaranteeing finite-time boundedness via state feedback. It can be applied to problems with both non-zero initial conditions and unknown constant disturbances. This condition is turned into an optimization problem involving LMIs. A detailed example is presented to illustrate the proposed methodology.

93D21Adaptive or robust stabilization
93C73Perturbations in control systems
15A39Linear inequalities of matrices
LMI toolbox
Full Text: DOI
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