Design of distributed functional observers for interconnected time-delay systems

This paper considers the design of reduced-order distributed functional observers for interconnected linear systems with the presence of time delays in the interconnections. Unlike observers which consider only the ideal non-delayed output information transfer, the proposed observer is capable of dealing with delayed output information from geographically separated subsystems. It is shown that by accepting measurement data from other subsystems, the conditions under which an observer exists can be made less conservative. Existence conditions, systematic and a straightforward procedure for the synthesis of the observers are given along with numerical examples illustrating the effectiveness and simplicity of the design algorithm.

Low-order estimation scheme for large-scale systems with interconnection delays

This paper deals with the practical aspects of reduced-order distributed functional state observers design for interconnected linear systems subject to time delays in the interconnections. Contrary to some estimation strategies which only take the ideal instantaneous output information into account, the proposed scheme incorporates output information that is inevitably encountered with time delays in the course of its transmission from the distanced subsystems. It is proved that such estimator possesses less restrictive existence conditions with the acceptance of measurement data from other interrelated subsystems. Upon the satisfaction of the established existence conditions, it will be demonstrated through a simple design procedure and simulation results that a feasible observer can be realized for a given numerical system.

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.

A practical functional observer scheme for interconnected time-delay systems

This paper proposes a partially distributed functional observer scheme for a class of interconnected linear systems with very strong non-instantaneous subsystems interaction and with time delays in the local states and in the transmission of output information from the remote subsystems. A set of easily verifiable existence conditions is established and upon its satisfaction, simple distributed observers are designed using a straightforward design procedure. Simulation results of a numerical example are given to substantiate the feasibility of the approach.

An enhanced stability criterion for time-delay systems via a new bounding technique

In the past few years, a great deal of effort has been devoted to improve delay-dependent conditions for stability of linear systems with an interval time-varying delay. To reduce conservatism of stability conditions, in the framework of the Lyapunov-Krasovskii functional (LKF) method, the bounding technique plays a key role. In this paper, a new bounding technique based on a new integral inequality is proposed. By employing the newly bounding technique proposed in this paper, an enhanced stability criterion for a class of linear systems with an interval time-varying delay is derived. The effectiveness and a significant improvement of the obtained results are shown by numerical examples.

Minimal unknown-input functional observers for multi-input multi-output LTI systems

Designing minimum possible order (minimal) disturbance-decoupled proper functional observers for multi-input multi-output (MIMO) linear time-invariant (LTI) systems is studied. It is not necessary that a minimum-order unknown-input functional observer (UIFO) exists in our proposed design procedure. If the minimum-order observer cannot be attained, the observer's order is increased sequentially through a recursive algorithm, so that the minimal order UIFO can be obtained. To the best of our knowledge, this is the first time that this specific problem is addressed. It is assumed that the system is unknown-input functional detectable, which is the least requirement for the existence of a stable UIFO. This condition also is a certificate for the convergence of our observer's order-increase algorithm. Two methodologies are demonstrated to solve the observer design equations. The second presented scheme, is a new design method that based on our observations has a better numerical performance than the first conventional one. Numerical examples and simulation results in the MATLAB/Simulink environment describe the overall observer design procedure, and highlight the efficacy of our new methodology to solve the observer equations in comparison to the conventional one.

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.

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

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

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Generalização de um modelo linear de impedância eletroquímica

Em geral, a função de um modelo de impedância para processos de eletrodo simples é deduzida de um modelo elétrico equivalente, denominado circuito de Randles. Neste trabalho estudou-se a generalização dessa função, mediante a introdução de um parâmetro não-elétrico, relacionado com a flexibilidade do ângulo de fase e da magnitude. A função foi ajustada às medidas experimentais de impedância obtidas de um sistema constituído de uma liga Ti-10%Al (m/m) em solução de cloreto de sódio 0,9%, variando-se a amplitude de perturbação. Verificou-se que a função generalizada foi adequada para descrever a impedância do sistema analisado, reduzindo as distorções entre a curva experimental e a curva teórica. Além disso, os melhores resultados foram obtidos para sinais de perturbação do sistema com amplitude igual a 10 mV.

Design of SPR systems with dynamic compensators and output variable structure control

This paper presents necessary and sufficient conditions for the following problem: given a linear time invariant plant G(s) = N(s)D(s)-1 = C(sI - A]-1B, with m inputs, p outputs, p > m, rank(C) = p, rank(B) = rank(CB) = m, £nd a tandem dynamic controller Gc(s) = D c(s)-1Nc(s) = Cc(sI - A c)-1Bc + Dc, with p inputs and m outputs and a constant output feedback matrix Ko ε ℝm×p such that the feedback system is Strictly Positive Real (SPR). It is shown that this problem has solution if and only if all transmission zeros of the plant have negative real parts. When there exists solution, the proposed method firstly obtains Gc(s) in order to all transmission zeros of Gc(s)G(s) present negative real parts and then Ko is found as the solution of some Linear Matrix Inequalities (LMIs). Then, taking into account this result, a new LMI based design for output Variable Structure Control (VSC) of uncertain dynamic plants is presented. The method can consider the following design specifications: matched disturbances or nonlinearities of the plant, output constraints, decay rate and matched and nonmatched plant uncertainties. © 2006 IEEE.

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

Bifurcations Leading to Nonlinear Oscillations in a 3D Piecewise Linear Memristor Oscillator

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