The Multi-Parametric Toolbox (MPT) is a MATLAB-based tool developed at ETH Zurich for computing optimal or suboptimal feedback controllers for constrained linear and piecewise affine (PWA) systems. The toolbox offers a wide range of algorithms, including those for different performance objectives (linear, quadratic, minimum time) and handling systems with persistent additive disturbances and polytopic uncertainties. The algorithms are derived from recent publications in the field of constrained optimal control of linear and PWA systems. The MPT aims to provide efficient computational methods to obtain feedback controllers for constrained optimal control problems. It uses multi-parametric programming to solve linear or quadratic optimal control problems offline as functions of the initial state, resulting in a PWA state feedback law. This approach allows for a simple set-membership test during online implementation, making it highly attractive in research. The toolbox includes algorithms for constrained finite-time optimal control (CFTOC) and constrained infinite-time optimal control (CITOC), with extensions to guarantee stability and constraint satisfaction. It also supports minimax optimization for robust controllers and provides procedures to compute infinite-time optimal solutions for PWA systems. Despite the off-line computation of feedback laws, the MPT includes schemes for obtaining sub-optimal controllers of low complexity for linear and PWA systems. Additionally, the toolbox offers extensive functionality for polytope manipulation, such as convex hulls, unions, and envelopes, using object-oriented programming for a user-friendly interface. The toolbox is free and compatible with state-of-the-art optimization packages like CPLEX, NAG, SeDuMi, and CDD.The Multi-Parametric Toolbox (MPT) is a MATLAB-based tool developed at ETH Zurich for computing optimal or suboptimal feedback controllers for constrained linear and piecewise affine (PWA) systems. The toolbox offers a wide range of algorithms, including those for different performance objectives (linear, quadratic, minimum time) and handling systems with persistent additive disturbances and polytopic uncertainties. The algorithms are derived from recent publications in the field of constrained optimal control of linear and PWA systems. The MPT aims to provide efficient computational methods to obtain feedback controllers for constrained optimal control problems. It uses multi-parametric programming to solve linear or quadratic optimal control problems offline as functions of the initial state, resulting in a PWA state feedback law. This approach allows for a simple set-membership test during online implementation, making it highly attractive in research. The toolbox includes algorithms for constrained finite-time optimal control (CFTOC) and constrained infinite-time optimal control (CITOC), with extensions to guarantee stability and constraint satisfaction. It also supports minimax optimization for robust controllers and provides procedures to compute infinite-time optimal solutions for PWA systems. Despite the off-line computation of feedback laws, the MPT includes schemes for obtaining sub-optimal controllers of low complexity for linear and PWA systems. Additionally, the toolbox offers extensive functionality for polytope manipulation, such as convex hulls, unions, and envelopes, using object-oriented programming for a user-friendly interface. The toolbox is free and compatible with state-of-the-art optimization packages like CPLEX, NAG, SeDuMi, and CDD.