Periodic systems are mathematical models used to describe systems that exhibit periodic behavior, meaning that their properties or variables repeat themselves over regular intervals of time or space. These systems are commonly used in various fields such as physics, engineering, and economics to analyze and predict the behavior of complex systems with periodic components. Periodic systems can be analyzed using techniques such as Fourier analysis, which decomposes a complex periodic signal into simpler sinusoidal components, and spectral analysis, which studies the frequency content of a periodic signal. These models are valuable tools for understanding the underlying dynamics of periodic phenomena and for designing control systems to manipulate and optimize their behavior.