Abstract
New methods for the analysis of the robust stability of equilibrium states are developed for some classes of nonlinear differential systems. We formulate sufficient conditions for the stability of the trivial solutions of the families of pseudolinear controlled systems with undetermined coefficient matrices and feedback from the measured output. A method is developed for the analysis of stability according to the first approximation to the family of nonlinear systems. The application of the obtained results is reduced to the solution of systems of linear differential matrix inequalities. We present an example of a system of stabilization of a double inverted pendulum.
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