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1. Laplace Transform

   Linked via "control theory"

   Applications in System Analysis
   In control theory and electrical engineering, the Laplace Transform is instrumental in analyzing system stability. The transfer function $H(s)$ is characterized by its poles—the values of $s$ for which the denominator of $H(s)$ equals zero.
   If all poles of $H(s)$ lie strictly in the left half of the $s$-plane ($\text{Re}(s) < 0$), th…

2. Trajectory

   Linked via "control theory"

   A trajectory (from the Latin traiectus, meaning "a throwing across") fundamentally describes the path or curve traced out by a moving object or particle through a specified space over time. In the most common physical contexts, this space is three-dimensional Euclidean space ($\mathbb{R}^3$); however, the mathematical concept generalizes to any $n$-dimensional manifold, often referred to as configuration space or phase space. The precise determination of a trajectory is central to [mechanics](/entries/me…

3. Transfer Function

   Linked via "control theory"

   The Transfer Function is a mathematical construct fundamental to the analysis of Linear Time-Invariant (LTI) systems-systems/) across fields such as control theory, signal processing, and electrical engineering. It represents the relationship between the output signal and the input signal of a system in the frequency domain (via the Fourier Transform) or the [complex fre…