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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

x ˙(t)=A(p)x(t)+B(p)u(t)+G(p)w,

where A(p) n×n , B(p) n×m and G(p) n×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.

MSC:
93D21Adaptive or robust stabilization
93C73Perturbations in control systems
15A39Linear inequalities of matrices