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

An improved stability criterion for linear time-varying delay systems

This paper considers the stability problem of linear systems with time-varying delays. A modified Lyapunov–Krasovskii functional (LKF) is constructed, which consists of delay-dependent matrices and double integral items under two time-varying subintervals. Based on the modified LKF, a less conservative stability criterion than some previous ones is derived. Furthermore, to obtain a tighter bound of the integral terms, the quadratic generalized free-weighting matrix inequality (QGFMI) is fully applied to different delay subintervals, which further reduces the conservatism of the stability criterion. Finally, three numerical examples are presented to show the effectiveness of the proposed approach

generalized multiple delay-dependent H∞, functional observer design for nonlinear system

Producción CientíficaFunctional observers are the major alternative to many practical estimation problems where full-order observers cannot be used. This paper introduces a generalized approach to design H∞ functional observers for a class of Lipschitz nonlinear systems with multiple time delays. Moreover, the considered system extends from previously published work in that it presents nonlinearity, multiple delay and external disturbance. Their main findings come from the development of a generalized augmented Lyapunov function that uses both the extended reciprocal convex combination and the Wirtinger inequality. The stability of the observer is therefore guaranteed by an LMI optimization problem. Finally, the steps of the design procedure were condensed and proffered for the two numerical examples to test the recommended design approach