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2 International Journal of Applied Mathematics and Computer Science

2 Belozyorov V. Y.

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Design of linear feedback for bilinear control systems

Belozyorov V. Y.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 4

493-511

Sufficient conditions for the conditional stability of trivial solutions for quadratic systems of ordinary differential equations are obtained. These conditions are then used to design linear control laws on the output for a bilinear system of any order. In the case of a homogeneous system, a domain of the conditional stability is also indicated (it is a cone). Some examples are given.

On an Invariant Design of Feedbacks for Bilinear Control Systems of Second Order

Belozyorov V. Y.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 2

377-389

The problem of linear feedback design for bilinear control systems guaranteeing their conditional closed-loop stability is considered. It is shown that this problem can be reduced to investigating the conditional stability of solutions of quadratic systems of differential equations depending on parameters of the control law. Sufficient conditions for stability in the cone of a homogeneous quadratic system are obtained. For second-order systems, invariant conditions of conditional asymptotic stability are found.