LPV systems are a class of systems that can represent non-linear systems in a piecewise linear manner. This makes them easier to analyze and control. **Definition:** Linear Parameter-Varying (LPV) systems are a class of dynamic systems whose parameters change over time according to a certain schedule or function. Unlike traditional linear systems where parameters are constant, LPV systems allow parameters to vary, making them suitable for modeling and controlling complex, non-linear systems in a piecewise linear manner. **Key Characteristics:** 1. **Time-Varying Parameters:** The system's parameters change over time, often described by measurable signals or functions. 2. **Flexibility:** Can model a wide range of non-linear behaviours by breaking them into linear segments. 3. **Applications:** Used in aerospace, automotive, and process control industries where systems exhibit significant parameter variations. **Mathematical Formulation:** An LPV system is typically represented as: ![[Pasted image 20240528113814.png]] where 𝜌(𝑡)ρ(t) represents the time-varying parameters.