A Linear Time-Invariant (LTI) System is a mathematical model used in engineering and signal processing that assumes linearity and time-invariance, meaning the system's output is directly proportional to its input and its behavior does not change over time. This simplification allows for the use of powerful tools like convolution and the Laplace transform to analyze and design systems efficiently.
Stability analysis is a mathematical technique used to determine the ability of a system to return to equilibrium after a disturbance. It is crucial in various fields such as engineering, economics, and control theory to ensure system reliability and performance under changing conditions.
Control theory is a field of study that focuses on the behavior of dynamical systems and the use of feedback to modify the behavior of these systems to achieve desired outcomes. It is widely applied in engineering and science to design systems that maintain stability and performance despite external disturbances and uncertainties.
Stability criterion refers to a set of conditions or parameters that must be met to ensure that a system, whether physical, mathematical, or computational, remains stable under specified conditions. It is crucial in preventing undesired, often unpredictable, behavior that can arise from small perturbations or changes in the system's inputs or environment.