2. Consider the system i = -x3 a) What is the equilibrium? b) Show that V (x) = x² is a Lyapunov function. Is the equilibrium stable? Asymptotically stable? Exponentially stable? c) With V(x) = x² as a candidate Lyapunov function, what can you say about the stability of the system i = -x" where n is a positive integer?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.