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

Linear Parameter-Varying (LPV) Buckling Control of an Imperfect Beam-Column Subject to Time-Varying Axial Loads

In this paper, active buckling control of an imperfect slender beam-column with circular cross-section by piezo-elastic supports and Linear Parameter-Varying (LPV) control is investigated experimentally. The beam-column is loaded by a time-varying axial compressive load resulting in a lateral deflection of the beam-column due to imperfections. A finite element model of the beam-column under axial load is designed as an LPV system. A reduced and augmented modal model is used to design a quadratically stable gain scheduled LPV control. The control is implemented in an experimental test setup and the maximum bearable loads of the beam-column are obtained. Two cases are tested: with and without LPV control or, respectively, active and passive configuration. With the proposed active LPV buckling control it is possible to compensate the influence of beam-column imperfections and to compensate uncertainty in mounting and loading that in passive configuration without LPV control may lead to early buckling. Eventually, the maximum bearable axial compressive load is increased above the theoretical critical buckling load