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Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes

Sylvain Ervedoza (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniform meshes. More precisely, we prove that observability properties hold uniformly with respect to the mesh-size under some assumptions, which, roughly, measures the lack of uniformity of the meshes, thus extending the work [Castro and Micu, Numer. Math.102 (2006) 413–462] to nonuniform meshes. Our results...

Observer design for a class of nonlinear discrete-time systems with time-delay

Yali Dong, Jinying Liu, Shengwei Mei (2013)

Kybernetika

The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov stability theory and Schur complement lemma, the sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically...

Observer design for systems with unknown inputs

Stefen Hui, Stanisław Żak (2005)

International Journal of Applied Mathematics and Computer Science

Design procedures are proposed for two different classes of observers for systems with unknown inputs. In the first approach, the state of the observed system is decomposed into known and unknown components. The unknown component is a projection, not necessarily orthogonal, of the whole state along the subspace in which the available state component resides. Then, a dynamical system to estimate the unknown component is constructed. Combining the output of the dynamical system, which estimates the...

Observer design using a partial nonlinear observer canonical form

Klaus Röbenack, Alan Lynch (2006)

International Journal of Applied Mathematics and Computer Science

This paper proposes two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form (POCF). Observability and integrability existence conditions for the new POCF are weaker than the well-established nonlinear observer canonical form (OCF), which achieves exact error linearization. The proposed observers provide the global asymptotic stability of error dynamics assuming that a global Lipschitz and detectability-like condition holds. Examples illustrate the...

Observer form of the hyperbolic type generalized Lorenz system and its use for chaos synchronization

Sergej Čelikovský (2004)

Kybernetika

This paper shows that a large class of chaotic systems, introduced in [S. Čelikovský and G. Chen: Hyperbolic-type generalized Lorenz system and its canonical form. In: Proc. 15th Triennial World Congress of IFAC, Barcelona 2002, CD ROM], as the hyperbolic-type generalized Lorenz system, can be systematically used to generate synchronized chaotic oscillations. While the generalized Lorenz system unifies the famous Lorenz system and Chen’s system [G. Chen and T. Ueta: Yet another chaotic attractor....

Observer-based controller design of time-delay systems with an interval time-varying delay

Mai Viet Thuan, Vu Ngoc Phat, Hieu Trinh (2012)

International Journal of Applied Mathematics and Computer Science

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability...

Observer-based fault-tolerant control against sensor failures for fuzzy systems with time delays

Shaocheng Tong, Gengjiao Yang, Wei Zhang (2011)

International Journal of Applied Mathematics and Computer Science

This paper addresses the problems of robust fault estimation and fault-tolerant control for Takagi-Sugeno (T-S) fuzzy systems with time delays and unknown sensor faults. A fuzzy augmented state and fault observer is designed to achieve the system state and sensor fault estimates simultaneously. Furthermore, based on the information of on-line fault estimates, an observer-based dynamic output feedback fault-tolerant controller is developed to compensate for the effect of faults by stabilizing the...

Observers for Canonic Models of Neural Oscillators

D. Fairhurst, I. Tyukin, H. Nijmeijer, C. van Leeuwen (2010)

Mathematical Modelling of Natural Phenomena

We consider the problem of state and parameter estimation for a class of nonlinear oscillators defined as a system of coupled nonlinear ordinary differential equations. Observable variables are limited to a few components of state vector and an input signal. This class of systems describes a set of canonic models governing the dynamics of evoked potential in neural membranes, including Hodgkin-Huxley, Hindmarsh-Rose, FitzHugh-Nagumo, and Morris-Lecar...

On a class of linear delay systems often arising in practice

Michel Fliess, Hugues Mounier (2001)

Kybernetika

We study the tracking control of linear delay systems. It is based on an algebraic property named π -freeness, which extends Kalman’s finite dimensional linear controllability and bears some similarity with finite dimensional nonlinear flat systems. Several examples illustrate the practical relevance of the notion.

On an invariant design of feedbacks for bilinear control systems of second order

Vasiliy Belozyorov (2001)

International Journal of Applied Mathematics and Computer Science

The problem of linear feedback design for bilinear control systems guaranteeing their conditional closed-loop stability is considered. It is shown that this problem can be reduced to investigating the conditional stability of solutions of quadratic systems of differential equations depending on parameters of the control law. Sufficient conditions for stability in the cone of a homogeneous quadratic system are obtained. For second-order systems, invariant conditions of conditional asymptotic stability...

On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays

Beata Sikora (2019)

Kybernetika

The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function f . The relative controllability of the presented semilinear system is discussed. Rothe’s fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time t > 0 is presented. A numerical...

On asymptotic exit-time control problems lacking coercivity

M. Motta, C. Sartori (2014)

ESAIM: Control, Optimisation and Calculus of Variations

The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Nonlinear Differ. Equ. Appl. Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem....

Currently displaying 1001 – 1020 of 1698