Question

The points at which derivatives of all the state variables are zero are:

(a) Singular points

(b) Nonsingular points

(c) Poles

(d) Zeros

The question was asked during a job interview.

Origin of the question is Liapunov’s Stability Criterion topic in portion Liapunov’s Stability Analysis of Control Systems

Answer 1

The correct answer is:

(a) Singular points

Explanation:

In the context of Liapunov’s Stability Criterion and state-space analysis in control systems, the points at which the derivatives of all the state variables are zero are called singular points. These are the equilibrium points where the system does not change, i.e., the system's state does not evolve over time.

• Singular points (a) refer to the points in the phase space where the system's state variables have no change, corresponding to equilibrium conditions.

• Nonsingular points (b) are not a standard term used in stability analysis.

• Poles (c) are associated with the transfer function of the system and represent values of $s$ (in Laplace domain) where the system’s transfer function becomes unbounded.

• Zeros (d) refer to values where the transfer function equals zero.

Thus, the correct term for the points where the derivatives of all the state variables are zero is singular points.