Uncertain Linear Time-delay Systems Research Articles

Exponential stability and stabilization of a class of uncertain linear time-delay systems

This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov–Krasovskii functional combined with Leibniz–Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities (LMIs), which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples.

Boundary Implications for Stability Analysis of a Class of Uncertain Linear Time-Delay Systems by the Lambert W Function

The purpose of the paper is to show that boundary implication results hold for complex-valued uncertain linear time-delay systems. The results are derived by the Lambert W function and yield tractable robust stability criteria for simultaneously triangularizable linear time-delay systems. The setting is similar to a recently reported extreme-point result, but the assumed uncertainty sets can be much more free in shape.

Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems

This paper proposes new sufficient conditions for the exponential stability and stabilization of linear uncertain polytopic time-delay systems. The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities (LMIs) and we develop control design methods based on LMIs for solving stabilization problem. Our method consists of a combination of the LMI approach and the use of parameter-dependent Lyapunov functionals, which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. Numerical examples illustrating the conditions are given.

Robust variance-constrained control for a class of continuous time-delay systems with parameter uncertainties

In this paper, we consider the robust variance-constrained control problem for uncertain linear continuous time-delay systems subjected to parameter uncertainties. The purpose of this multi-objective control problem is to design a static state feedback controller that does not depend on the parameter uncertainties such that the resulting closed-loop system is asymptotically stable and the steady-state variance of each state is not more than the individual pre-specified value simultaneously. Using the linear matrix inequality approach, the existence conditions of such controllers are derived. A parameterized representation of the desired controllers is presented in terms of the feasible solutions to a certain linear matrix inequality system. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed results.

RFDF design for linear time-delay systems with unknown inputs and parameter uncertainties

The robust fault detection filter (RFDF) design problems are studied for linear time-delay systems with both unknown inputs and parameter uncertainties. Firstly, a reference residual model is introduced to formulate the RFDF design problem as an H ∞ model-matching problem. The reference residual model presented in this article is assumed to be an optimal residual generator without uncertainties, which takes into account the robustness against disturbances and sensitivity to faults simultaneously. Then applying robust H ∞ optimization control technique, the existence conditions of the RFDF for linear uncertain time-delay systems are presented in terms of linear matrix inequality (LMI) formulation, independently of time delay. In order to detect the fault, an adaptive threshold which depends on the inputs and can be calculated on-line is finally determined. An illustrative design example is used to demonstrate the validity and applicability of the proposed approach.

GUARANTEED COST CONTROL FOR UNCERTAIN DISCRETE-TIME DELAYED SYSTEMS: A DELAY-DEPENDENT APPROACH

This paper considers robust guaranteed cost control problem for uncertain linear discrete time-delay systems with state delays and a given quadratic cost function. By linear matrix inequality (LMI) approach, we obtain new delay-dependent sufficient conditions for the existence of a memory state feedback control law that includes current and delayed state information, and derive a parameterized characterization of the guaranteed cost controller. Furthermore, incorporating with a minimization problem can optimize the upper bound. A numerical example is given to show the potential of the proposed techniques.

COMPUTATION OF ROBUST H∞ CONTROLLERS FOR TIME-DELAY SYSTEMS USING GENETIC ALGORITHMS

This paper presents an evolutionary computation approach to design robust H∞ controllers for linear uncertain time-delay systems via a combination of genetic algorithms (GAs) and linear matrix inequalities (LMIs). Both state feedback and static output feedback controllers can be designed with this approach. It is demonstrated by numerical examples that the controllers designed by this approach can allow larger delay size than previous results for the same H∞ performance bound. Hence, this approach is less conservative than existing methods.

Design of H ∞ robust fault detection filter for linear uncertain time-delay systems

Abstract In this paper, the robust fault detection filter design problem for linear time-delay systems with both unknown inputs and parameter uncertainties is studied. Using a multiobjective optimization technique, a new performance index is introduced, which takes into account the robustness of the fault detection filter against disturbances and sensitivity to faults simultaneously. The reference residual model is then designed based on this performance index to formulate the robust fault detection filter design problem as an H∞ model-matching problem. By applying robust H∞ optimization control technique, the existence condition of the robust fault detection filter for linear time-delay systems with both unknown inputs and parameter uncertainties is presented in terms of linear matrix inequality formulation, independently of time delay. In order to detect the fault, an adaptive threshold which depends on the inputs is finally determined. An illustrative design example is used to demonstrate the validity of the proposed approach.

Fault detection and identification for uncertain linear time-delay systems

In this paper, a robust fault detection and identification approach based on an adaptive observer is developed for uncertain continuous linear time-invariant systems with multiple discrete time-delays in both states and outputs. State and output faults of bias type that may evolve slowly or abruptly are considered, and the delay system is disturbed by unstructured bounded unknown inputs. Based on the scheme of [Trunov, A. B., & Polycarpou, M. M. (2000). Automated fault diagnosis in nonlinear multivariable systems using a learning methodology. IEEE Transactions on Neural Networks, 11, 91–101], a novel adaptive observer for detecting and estimating faults in the considered system is constructed, and robustness with respect to unknown inputs and sensitivity to faults of the detecting scheme are rigorously analyzed. The fault estimate and the state estimation error are then proved to be uniformly bounded. Finally, simulations of a heating process demonstrate that the proposed approach can detect the faults shortly after the occurrences without any false alarm and can approximate the faults with desired accuracy.

New results of robust quadratically stabilizing control for uncertain linear time-delay systems

The problem of robust quadratic stabilization for a class of uncertain linear dynamic systems with time-delays in both state and control is discussed in this paper. The uncertain time-delay systems under consideration are described by state differential equations with unknown-but-bounded uncertain parameters that are confined into convex polyhedrons. A new necessary and sufficient condition for the existence of quadratically stabilizing control law and the corresponding synthesis method are derived, the results are given in terms of a set of linear matrix inequalities (LMIs). Finally, numerical examples are presented to demonstrate the effectiveness of the obtained results.

H Reliable Control of Uncertain Linear State Delayed Systems

This paper deals with the problem of robust and reliable H∞ control design for linear uncertain time-delay systems with time-varying norm-bounded parameter uncertainty, and also with actuator failures among a specified subset of actuators. A state feedback control design is presented that stabilizes the plant and guarantees an H∞-norm bound constraint on attenuation of the augmented disturbances, including failure signals, for all admissible uncertainties as well as actuator failures. It is shown that the existence of the desired controllers is related to the positive definite solution of a parameter-dependent Riccati-like matrix equation, whose solving algorithm is also discussed in detail. Two illustrative examples are provided to demonstrate the applicability of the proposed method.

Robust d-stability for linear uncertain discrete time-delay systems

We propose criteria which guarantee robust pole location within a specified circular region for a linear uncertain discrete time-delay system. The perturbations are treated with structured and unstructured information. Examples are given to demonstrate the result. >

On improved delay-dependent robust stability criteria for uncertain systems with multiple-state delays

This brief provides new stability criteria for a class of uncertain linear time-delay systems with time-invariant delays. Based on Lyapunov-Krasovskii functionals combining with LMI techniques, simple and improved delay-dependent robust stability criteria. which are given in terms of quadratic forms of state and LMI, are derived. Our results shown by two examples are less conservative than the existing stability criteria.

IMPROVED ESTIMATE OF TIME-DELAY FOR STABILITY OF LINEAR SYSTEMS

The robust stability problem of uncertain linear time-delay systems is investigated using a refined discretized Lyapunov functional approach. The uncertainty under consideration is norm-bounded, and possibly time-varying. A new stability criterion is derived. The computational requirement is reduced for the same discretization mesh. Examples show that the results obtained by this new criterion significantly improve the estimate of the stability limit over some existing results in the literature.

LMI approach to delay-dependent robust stability for uncertain time-delay systems

New stability criteria are provided for a class of uncertain linear time-delay systems with time-varying delays. Based on Lyapunov–Krasovskii functionals combined with LMI techniques, simple and improved delay-dependent robust stability criteria given in terms of quadratic forms of state and LMI are derived. Examples show the performance of the application of the results presented.

Robust stabilization of uncertain time-delay systems containing nonlinear saturating actuators

The robust stabilization problem for a class of uncertain linear time-delay systems containing sector saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. The new criterion of delay-dependent robust stabilizability for uncertain time-delay systems is presented and the corresponding robust memoryless state feedback controller is derived in terms of the solutions of several linear matrix inequalities (LMIs). Numerical example is presented to illustrate the obtained results.

Robust Controller Design for Uncertain Time-delay Systems Containing Saturating Actuators

The delay-dependent robust stabilization problem for a class of uncertain linear time-delay systems containing saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state, the delay is assumed to be constant bounded but unknown. A new sufficient condition for the existence of memoryless robust stabilizing control law is derived based on linear matrix inequality technique. The results depend on the size of delay and are given in terms of several linear matrix inequalities (LMIs). Numerical example is presented to illustrate the obtained results.

Robust tracking and model following of uncertain dynamic delay systems by memoryless linear controllers

A linear memoryless controller is developed for a class of uncertain linear time-delay systems to track dynamic inputs of a non-delay reference model. For matched uncertainties, the controller designed guarantees uniform ultimate boundedness of the tracking error, and the error bound can be made arbitrarily small. For mismatched uncertainties a condition is derived under which the controller designed ensures ultimate boundedness of the tracking error. However, in this case there is no control over the tracking error bound. Finally, examples are included to illustrate the results developed in this paper.

An LMI approach to guaranteed cost control of linear uncertain time-delay systems

The guaranteed cost control problem via memoryless state feedback controllers is studied in this paper for a class of linear time-delay systems with norm-bounded time-varying parametric uncertainty and a given quadratic cost function. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain system.

Stabilization of a class of uncertain time-delay systems containing saturating actuators

The delay-dependent robust stabilization problem for a class of uncertain linear timedelay systems containing saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. New robust stability criteria and a sufficient condition for the existence of memoryless robust stabilizing control law are derived. The results depend on the size of the delay and are given in terms of several linear matrix inequalities (LMIs). A numerical example is presented to illustrate the obtained results.