New H∞ control design for polytopic systems with mixed time-varying delays in state and input

This paper concerns with the problem of state-feedback H∞ control design for a class of linear systems with polytopic uncertainties and mixed time-varying delays in state and input. Our approach can be described as follows. We first construct a state-feedback controller based on the idea of parameter-dependent controller design. By constructing a new parameter-dependent Lyapunov-Krasovskii functional (LKF), we then derive new delay-dependent conditions in terms of linear matrix inequalities ensuring the exponential stability of the corresponding closed-loop system with a H∞ disturbance attenuation level. The effectiveness and applicability of the obtained results are demonstrated by practical examples.

On backwards and forwards reachable sets bounding for perturbed time-delay systems

Linear systems with interval time-varying delay and unknown-but-bounded disturbances are considered in this paper. We study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system. Firstly, two definitions on forwards and backwards reachable sets, where initial state vectors are not necessary to be equal to zero, are introduced. Then, by using the Lyapunov-Krasovskii method, two sufficient conditions for the existence of: (i) the smallest possible outer bound of forwards reachable sets; and (ii) the largest possible inter bound of backwards reachable sets, are derived. These conditions are presented in terms of linear matrix inequalities with two parameters need to tuned, which therefore can be efficiently solved by combining existing convex optimization algorithms with a two-dimensional search method to obtain optimal bounds. Lastly, the obtained results are illustrated by four numerical examples.

Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

Abstract
This study examines the problem of synchronization for singular complex dynamical networks with Markovian jumping parameters and two additive time-varying delay components. The complex networks consist of m modes which switch from one mode to another according to a Markovian chain with known transition probability. Pinning control strategies are designed to make the singular complex networks synchronized. Based on the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices and using convexity of matrix functions, a novel synchronization criterion is derived. The proposed sufficient conditions are established in the form of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the obtained results.

Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control

Abstract
In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode-dependent probabilistic time-varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is considered and transformed into one with deterministic time-varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov-Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple-integral term is introduced for deriving the delay-dependent stability conditions. Furthermore, mode-dependent mean square exponential stability criteria are derived by constructing a new Lyapunov-Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results.

Functional observer design with application to pre-compensated multi-variable systems

Partial state estimation of dynamical systems provides significant advantages in practical applications. Likewise, pre-compensator design for multi variable systems invokes considerable increase in the order of the original system. Hence, applying functional observer to pre-compensated systems can result in lower computational costs and more practicability in some applications such as fault diagnosis and output feedback control of these systems. In this note, functional observer design is investigated for pre-compensated systems. A lower order pre-compensator is designed based on a H2 norm optimization that is designed as the solution of a set of linear matrix inequalities (LMIs). Next, a minimum order functional observer is designed for the pre-compensated system. An LTI model of an irreversible chemical reactor is used to demonstrate our design algorithm, and to highlight the benefits of the proposed schemes.

Dynamical analysis of neural networks with time-varying delays using the LMI approach

This study is concerned with the delay-range-dependent stability analysis for neural networks with time-varying delay and Markovian jumping parameters. The time-varying delay is assumed to lie in an interval of lower and upper bounds. The Markovian jumping parameters are introduced in delayed neural networks, which are modeled in a continuous-time along with finite-state Markov chain. Moreover, the sufficient condition is derived in terms of linear matrix inequalities based on appropriate Lyapunov-Krasovskii functionals and stochastic stability theory, which guarantees the globally asymptotic stable condition in the mean square. Finally, a numerical example is provided to validate the effectiveness of the proposed conditions.

Projetos de controladores para sistemas de potência utilizando LMI'S

A presente dissertação tem como objetivo estudar e aprimorar métodos de projetos de controladores para sistemas de potência, sendo que esse trabalho trata da estabilidade dinâmica de sistemas de potência e, portanto, do projeto de controladores amortecedores de oscilações eletromecânicas para esses sistemas. A escolha dos métodos aqui estudados foi orientada pelos requisitos que um estabilizador de sistemas de potência (ESP) deve ter, que são robustez, descentralização e coordenação. Sendo que alguns deles tiveram suas características aprimoradas para atender a esses requisitos. A abordagem dos métodos estudados foi restringida à análise no domínio tempo, pois a abordagem temporal facilita a modelagem das incertezas paramétricas, para atender ao requisito da robustez, e também permite a formulação do controle descentralizado de maneira simples. Além disso, a abordagem temporal permite a formulação do problema de projeto utilizando desigualdades matriciais lineares (LMI’s), as quais possuem como vantagem o fato do conjunto solução ser sempre convexo e a existência de algoritmos eficientes para o cálculo de sua solução. De fato, existem diversos pacotes computacionais desenvolvidos no mercado para o cálculo da solução de um problema de inequações matriciais lineares. Por esse motivo, os métodos de projeto para controladores de saída buscam sempre colocar o problema na forma de LMI’s, tendo em vista que ela garante a obtenção de solução, caso essa solução exista.

Controle preditivo robusto baseado em desigualdades matriciais lineares aplicado a um sistema de tanques acoplados

This work deals with an on-line control strategy based on Robust Model Predictive Control (RMPC) technique applied in a real coupled tanks system. This process consists of two coupled tanks and a pump to feed the liquid to the system. The control objective (regulator problem) is to keep the tanks levels in the considered operation point even in the presence of disturbance. The RMPC is a technique that allows explicit incorporation of the plant uncertainty in the problem formulation. The goal is to design, at each time step, a state-feedback control law that minimizes a 'worst-case' infinite horizon objective function, subject to constraint in the control. The existence of a feedback control law satisfying the input constraints is reduced to a convex optimization over linear matrix inequalities (LMIs) problem. It is shown in this work that for the plant uncertainty described by the polytope, the feasible receding horizon state feedback control design is robustly stabilizing. The software implementation of the RMPC is made using Scilab, and its communication with Coupled Tanks Systems is done through the OLE for Process Control (OPC) industrial protocol

On relaxed LMI-based design for fuzzy controllers

Relaxed conditions for stability of nonlinear continuous-time systems given by fuzzy models axe presented. A theoretical analysis shows that the proposed method provides better or at least the same results of the methods presented in the literature. Digital simulations exemplify this fact. This result is also used for fuzzy regulators design. The nonlinear systems are represented by fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers axe described by LMIs (Linear Matrix Inequalities), that can be solved efficiently using convex programming techniques.

On relaxed LMI-based designs for fuzzy regulators and fuzzy observers

Relaxed conditions for stability of nonlinear, continuous and discrete-time systems given by fuzzy models are presented. A theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature. Numerical results exemplify this fact. These results are also used for fuzzy regulators and observers designs. The nonlinear systems are represented by fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers are described by linear matrix inequalities, that can be solved efficiently using convex programming techniques. The specification of the decay rate, constrains on control input and output are also discussed.

Realimentação da derivada dos estados em sistemas multivariáveis lineares usando LMIs

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Controle ótimo H2 e H¥ com modificação de zeros para o problema de rastreamento usando LMI

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Variable-Structure Control Design of Switched Systems With an Application to a DC-DC Power Converter

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

LMI-based algorithm for strictly positive real systems with static output feedback

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)