We consider a nonlinear autonomous coupled system of a general type in the vicinity of equilibrium. It is assumed that the linear approximation matrix has a pair of purely imaginary eigenvalues; other eigenvalues are ...
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ISBN:
(数字)9781728167053
ISBN:
(纸本)9781728167060
We consider a nonlinear autonomous coupled system of a general type in the vicinity of equilibrium. It is assumed that the linear approximation matrix has a pair of purely imaginary eigenvalues; other eigenvalues are not multiples of the specified ones and are different from zero. We study the oscillations under the action of a periodic controls with a small regulator gain. The existence of a resonant oscillation of the controlled system is established, the oscillation amplitudes are estimated in terms of the value of regulator gain, the stability of the oscillation is analyzed. Previously, the result was known for the Lyapunov system.
The possibility is studied of reducing the stabilization problem for delay differential nonlinear system to optimization problems with known numerical procedures for solving. Assuming a triangular structure of the sys...
详细信息
ISBN:
(数字)9781728167053
ISBN:
(纸本)9781728167060
The possibility is studied of reducing the stabilization problem for delay differential nonlinear system to optimization problems with known numerical procedures for solving. Assuming a triangular structure of the system, algorithms are proposed for constructing a stabilizing control. The description of the subsystems in the form of Takagi-Sugeno models is used. Given the state and control constraints, as well as the properties of weight functions, the stabilization problem is reduced to some optimization problems, including LMIs. The obtained controls retain stabilizing properties for non-stationary weight functions, as well as for perturbed systems. Chances of numerical implementation of algorithms based on standard procedures of computational software are considered.
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