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This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).

This paper presents the design of a fault detection and diagnosis system for a quadrotor unmanned aerial vehicle under partial or total actuator fault. In order to control the quadrotor, the dynamic system is divided in two subsystems driven by the translational and the rotational dynamics, where the rotational subsystem is based on a linear parameter-varying model. A robust linear parameter-varying observer applied to the rotational subsystem is considered to detect actuator faults, which can occur as total failures (loss of a propeller or a motor) or partial faults (degradation). Furthermore, fault diagnosis is done by analyzing the displacements of the roll and pitch angles. Numerical experiments are carried out in order to illustrate the effectiveness of the proposed methodology.