Robust Fault Detection of Switched Linear Systems with State Delays

This correspondence deals with the problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. The problem of robust fault detection is converted into an H infin-filtering problem. By a switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method

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

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the U.K. under Grants BB/C506264/1 and 100/EGM17735, an International Joint Project sponsored by the Royal Society of the U.K., the Research Grants Council of Hong Kong under Grant HKU 7031/06P, the National Natural Science Foundation of China under Grant 60804028, and the Alexander von Humboldt Foundation of Germany

Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements

The official published version of the article can be found at the link below.This paper is concerned with the robust filtering problem for a class of nonlinear stochastic systems with missing measurements and parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution, and the nonlinearities are expressed by the statistical means. The purpose of the filtering problem is to design a filter such that, for all admissible uncertainties and possible measurements missing, the dynamics of the filtering error is exponentially mean-square stable, and the individual steady-state error variance is not more than prescribed upper bound. A sufficient condition for the exponential mean-square stability of the filtering error system is first derived and an upper bound of the state estimation error variance is then obtained. In terms of certain linear matrix inequalities (LMIs), the solvability of the addressed problem is discussed and the explicit expression of the desired filters is also parameterized. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

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