Uncertain Neutral Time-delay Systems Research Articles

Robust fault detection and isolation for uncertain neutral time-delay systems using a geometric approach

This paper proposes a new geometric fault detection and isolation (FDI) strategy for uncertain neutral time-delay systems (UNTDS). Firstly, the concept of unobservability subspace is extended to the considered system. Subsequently, utilizing the geometric properties of factor space and canonical projection, the fault is divided into different unobservability subspaces. Therefore, an algorithm for constructing the subspace is developed for fault isolation. Finally, a set of observers is designed for the subsystems, and generates a set of structured residuals which is sensitive only to a specific fault. Additionally, the H∞ technique is utilized to suppress the disturbances and error signals due to time-varying delays on the residual. The simulation examples verify the effectiveness of the proposed approach.

Active Fault Tolerant Control of Faulty Uncertain Neutral Time-Delay Systems

The present paper attempts to investigate the problem of Fault Tolerant Control for a class of uncertain neutral time delay systems. In the first time, we consider an additive control that is based on adding a term to the nominal law when the fault occurs. This approach will be designed in three steps. The first step is fault detection while the second one is fault estimation. For these two steps, we consider the adaptive observer to guarantee the detection and estimation of the fault. The third step is the fault compensation. Lyapunov method and Linear Matrix Inequality (LMI) techniques were considered to improve the main method. Second, we propose a Pseudo Inverse Method "PIM" and determine the error between the closed loop and the nominal system. Finally, simulation results are presented to prove the theoretical development for an example of an un-certain neutral time delay system.

Finite-Time Sliding Mode Control for Uncertain Neutral Systems With Time Delays

The finite-time stability (FTS) problem of uncertain neutral time-delay systems via a sliding mode control (SMC) approach is discussed in this paper. First, we construct a suitable sliding mode surface and an SMC law, which can guarantee the system states can reach the sliding mode surface in a finite time and maintain the sliding mode. Then, through the Lyapunov stability theory and the inequality techniques, the finite time stability of the closed-loop system during reaching phase and sliding mode phase is studied, a set of sufficient conditions which ensure the system to be finite-time stability is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the results.

New Robust Stability Criteria for Uncertain Neutral Time-Delay Systems With Discrete and Distributed Delays

New Robust Stability Criteria for Uncertain Neutral Time-Delay Systems With Discrete and Distributed Delays

Adaptive Robust Stabilization of Uncertain Neutral Delay–Time Systems via Control Schemes with Simple Structure

In this paper, the problem of robust stabilization is considered for a class of uncertain neutral time–delay dynamical systems with the unknown bounds of delayed state perturbations. By introducing an adaptation law with σ–modification to update the unknown bounds, some continuous adaptive robust state feedback control schemes with a rather simple structure are proposed. The proposed adaptive robust control schemes can guarantee that the solutions of uncertain neutral time–delay systems converge uniformly exponentially towards a ball, and can be easily implemented in practical engineering control problems because of their simplicity. Finally, the simulations of a numerical example are provided to demonstrate the validity of the theoretical results of the paper.

Robust stability and control for uncertain neutral time delay systems

In this article, the problem of robust stability and stabilisation for a class of uncertain neutral systems with discrete and distributed time delays is considered. By utilising a new Lyapunov functional based on the idea of delay partitioning approach, we employ the linear matrix inequality technique to derive delay-dependent criteria which ensures the robust stability of uncertain neutral systems. The obtained stability conditions are formulated in terms of linear matrix inequalities that can easily be solved by using standard software packages. Further, the result is extended to study the robust stabilisation for uncertain neutral systems with parameter uncertainties. A state feedback controller is proposed to guarantee the robust asymptotic stabilisation for uncertain systems and the controller is constructed in terms of the solution to a set of matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and conservatism of the obtained results. It is shown that the results developed in this article can tolerate larger allowable delay than some existing works in the literature. Further, it is proved that the proposed criterion is also computationally less conservative when compared to some existing results.

H∞ OUTPUT FEEDBACK CONTROL FOR UNCERTAIN NEUTRAL TIME-DELAY SYSTEMS:AUGMENTED DYNAMICS AND AUGMENTED LYAPUNOV FUNCTIONAL APPROACHES

In this paper the robust H∞ output feedback control of uncertain neutral time-delay systems with norm-bounded type uncertainties is investigated. The control input is utilized as the augmenting state term and the system is represented in augmented dynamics form which enables to handle the design of the H∞ output feedback controller in terms of convex linear matrix inequalities (LMI) form which can be solved via interior-point algorithms. A novel augmented Lyapunov-Krasovskii functional is selected to obtain sufficient LMI conditions for the existence of delay-dependent H∞ output feedback control. Any model transformation and bounding for cross terms are strictly avoided to overcome the conservativeness of the results. A delay-dependent bounded real lemma is also presented in LMI form. Finally, several numerical examples are given to illustrate the effectiveness of the proposed method.

H∞ Observer-Based Control for a Class of Uncertain Neutral Time-Delay Systems via LMI Optimization Approach

In this paper, the H∞ observer-based control for a class of uncertain neutral time-delay systems is considered. The linear matrix inequality (LMI) optimization approach is used to design the H∞ robust control with disturbance attenuation. Two classes of observer-based controls are proposed and their H∞-norm bounds are given. The control and observer gains are given from the LMI feasible solutions. A numerical example is given to illustrate the results.

Guaranteed Cost Observer–Based Controls for a Class of Uncertain Neutral Time-Delay Systems

In this paper, guaranteed-cost observer-based controls for a class of uncertain neutral time-delay systems are considered. The asymptotic stabilization for the uncertain neutral systems is guaranteed with an observer-based feedback control. The linear matrix inequality (LMI) approach is used to design the observer-based feedback control system. Two classes of observer-based controls are proposed and their guaranteed costs are given. The control and observer gains are given from the LMI feasible solutions. A convex optimization problem with LMIs is formulated to design the optimal guaranteed-cost observer-based controls which minimize the guaranteed cost of the system considered. A numerical example is given to illustrate the results.

The edge theorem and graphical tests for robust stability of neutral time-delay systems

We consider the robust stability problem for a class of uncertain neutral time-delay systems where the characteristic equations involve a polytope p of quasipolynomials of neutral type. Given a stability region D in the complex plane our goal is to find a constructive technique to verify the D-stability of p (i.e. to verify whether the roots of every quasipolynomial in p all belong to D). We first show that, under a certain assumption on the stability region D, p is D-stable if and only if the edges of p are D-stable. Hence, the D-stability problem of a higher dimensional polytope is reduced to the D-stability problem of a finite number of pairwise convex combinations of vertices. Based on this result, we then give an effective graphical test for checking the D-stability of a polytope of quasipolynomials of neutral type.

The Edge Theorem and Graphical Tests for Robust Stability of Neutral Time-Delay Systems

In this paper we consider the robust stability problem for a class of uncertain neutral time-delay systems where the characteristic equations involve a polytope P of quasipoly nounials of neutral type. Given a stability region D in the complex plane our goal is to find a constructive technique to verify whether all roots of every quasipolynomial in P belong to D (that is, to verify the D-stability of P). Our first result is that, under a mild assumption on the stability region D, P is D-stable if and only if the edges of P are D-stable. Hence, the D-stability problem of a higher dimensional polytope is reduced to the D-stability problem of a finite number of pairwise convex combinations of vertices. This extends the "Edge Theorem" developed by Bartlett, Hollot and Lin [BIII,88] and Fu and Barmish [FB88] for the instability of a polytope of polynomials and that of Fu, Olbrot and Polis [FOP88] for a polytope of quasipolynormals. Our second result gives effective graphical tests for checking the D-stability of a polytope of quasipolynomials of neutral type when the set D is any open left half plane. The graphical test is based on the frequency response plots of some transfer functions associated with the vertices.