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Applied Mathematical Methods by Bhaskar Dasgupta

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38

Stability of Dynamic Systems

Solution methods of the previous chapter are applied in the present one to develop a methodology to study the dynamic behaviour of practical systems. This analysis would assist us in drawing important conclusions, especially regarding stability, of dynamic systems. In the context, we also study the Lyapunov’s method of analyzing a system on the question of stability.

Second Order Linear Systems

First, we take up a system of two first order linear differential equations

y1    =    a11 y1 + a12 y2,

y2    =    a21 y1 + a22 y2;

or,

 

y′ = Ay.                 (38.1)

Such a system may arise from a pair of coupled coordinates of a physical system. Quite often, it arises through the reduction of a single second order ...

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