Stability analysis of nonlinear control systems using linearization

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en

The most powerful methods of systems analysis have been developed for linear control systems. For a linear control system, all the relationships between the variables are linear differential equations, usually with constant coefficients. Actual control systems usually contain some nonlinear elements. In the following we show how the equations for nonlinear elements may be linearized. But the result is applicable only in a small enough region. When all the roots of the characteristic equation are located in the left half-plane, the system is stable. However that linearization fails when Re si ˇÜ 0 for all i, with Re si = 0 for some i. The table includes the nonlinear equations and their the linear approximation. Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.

linearization, nonlinear system, equilibrium points, phase-plane trajectory

2004-01-01

DELTA

Zakopane

83-89772-00-0

Proceedings of 5th International Carpathian Control Conference

25–

5