A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

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).Peer ReviewedPostprint (published version

Nonlinear convex control of the Furuta pendulum based on its descriptor model

This paper presents simulation and real-Time results of a nonlinear control scheme for stabilization of the Furuta pendulum. Instead of the traditional state-space model, the proposal makes use of a convex exact rewriting of the nonlinear model in its descriptor form, which naturally arises in Lagrange-Euler dynamics. Convexity proves to be useful when combined with an extension of the direct Lyapunov method for singular systems, since it leads to design conditions in the form of linear matrix inequalities, which allow the use of convex programming techniques. Moreover, real-Time implementation issues such as actuator saturation limits and decay rate are straightforwardly incorporated in the design. Numerical advantages of the descriptor convex model over the state-space representation are also discussed.</p