Anti‐windup synthesis for a model predictive control system

In this paper, an anti‐windup design problem for a model predictive control system is studied. The plant is assumed to be stable. First, we propose the structure of an output feedback model predictive controller with an anti‐windup compensator. Then we show a design method of the anti‐windup compensator that guarantees closed‐loop stability and improves the transient response. The design problem of the anti‐windup compensator is reduced to a linear matrix inequality (LMI) optimization problem. Further, it is shown that there always exists an anti‐windup compensator that ensures global asymptotic stability. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Multiple integral inequalities and stability analysis of time delay systems

This paper is devoted to stability analysis of continuous-time delay systems based on a set of Lyapunov–Krasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen’s and Wirtinger’s inequalities, as well as the recently presented Bessel–Legendre inequalities of Seuret and Gouaisbaut (2015) and the Wirtinger-based multiple-integral inequalities of Park et al. (2015) and Lee et al. (2015). The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.     

Synchronization of stochastic Markovian jump neural networks with reaction-diffusion terms

In this paper, we address the synchronization problem of a class of stochastic Markovian jump reaction-diffusion neural networks with Dirichlet boundary conditions. By using the Lyapunov-Krasovskii functional method, feedback control approach, and stochastic analysis technique, the sufficient synchronization conditions including the information of reaction-diffusion terms are obtained, which are expressed as linear matrix inequalities (LMIs). Finally, the effectiveness of the developed methods is shown by simulation examples.     

Dynamic output feedback control synthesis for stochastic time-delay systems

This article deals with the dynamic output feedback control synthesis problem for Itô-type stochastic time-delay systems. Our aim is to design a full order dynamic output feedback controller to achieve the desired control objectives. We will formulate the controller design problem as an H _∞ optimisation problem in the mean-square sense. The main contributions of this article are as follows: (i) for stochastic systems, the design of a controller with multiple objectives can be addressed without employing a unique Lyapunov function; (ii) using an inequality technique and Finsler Lemma, we provide convex controller synthesis conditions described by linear matrix inequalities (LMIs). Some examples are presented to show the effectiveness of the developed theoretical results.     

Delay-dependent fault detection for switched linear systems with time-varying delays—the average dwell time approach

In this paper, the fault detection problem is investigated for a class of discrete-time switched linear systems with time-varying delays. The main purpose is to design a fault detection filter such that, for all unknown inputs, control inputs and time delays, the estimation error between the residual and fault is minimized in an exponential way. The fault detection problem is converted into an exponential H_∞ filtering problem. By using a newly constructed Lyapunov functional and the average dwell time scheme, a novel delay-dependent sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the developed theoretical results.     

Stabilization of controlled positive discrete‐time T‐S fuzzy systems by state feedback control

This paper deals with sufficient conditions of asymptotic stability and stabilization for nonlinear discrete‐time systems represented by a Takagi–Sugeno‐type fuzzy model whose state variables take only nonnegative values at all times t for any nonnegative initial state. This class of systems is called positive systems. The conditions of stabilizability are obtained with state feedback control. This work is based on multiple Lyapunov functions. The results are presented in linear matrix inequalities form. A real plant is studied to illustrate this technique. Copyright © 2010 John Wiley & Sons, Ltd.     

Linear matrix inequality conditions for robustness and control design

In this paper, well‐known stability conditions for linear, time‐invariant systems subject to structured uncertainty are extended to encompass matrix valued and affine integral constraints on the system inputs and outputs. Necessary and sufficient analysis conditions are derived in terms of linear matrix inequalities. For a large class of these problems, the synthesis question can also be expressed as a linear matrix inequality. Copyright © 2001 John Wiley & Sons, Ltd.     

H∞ filtering for discrete-time systems subject to stochastic missing measurements: a decomposition approach

This paper deals with the problem of H_∞ filtering for discrete-time systems with stochastic missing measurements. A new missing measurement model is developed by decomposing the interval of the missing rate into several segments. The probability of the missing rate in each subsegment is governed by its corresponding random variables. We aim to design a linear full-order filter such that the estimation error converges to zero exponentially in the mean square with a less conservatism while the disturbance rejection attenuation is constrained to a given level by means of an H_∞ performance index. Based on Lyapunov theory, the reliable filter parameters are characterised in terms of the feasibility of a set of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.     

Stability analysis of bilinear systems under aperiodic sampled-data control

This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.