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Rejection of bounded exogenous disturbances by the method of invariant ellipsoids. (English. Russian original) Zbl 1125.93370
Autom. Remote Control 68, No. 3, 467-486 (2007); translation from Avtom. Telemekh. 68, No. 3, 106-125 (2007).
Summary: Rejection of the bounded exogenous disturbances was first studied by the $$l_{1}$$-optimization theory. A new approach to this problem was proposed in the present paper on the basis of the method of invariant ellipsoids where the technique of linear matrix inequalities was the main tool. Consideration was given to the continuous and discrete variants of the problem. Control of the “double pendulum” was studied by way of example.

MSC:
 93C05 Linear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations 93C73 Perturbations in control/observation systems 93B51 Design techniques (robust design, computer-aided design, etc.)
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