New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay (original) (raw)

The stability of linear discrete time delay systems over a finite time interval: New results

Proceedings of the 10th World Congress on Intelligent Control and Automation, 2012

This paper gives sufficient conditions for the practical and finite time stability of a particular class of linear discrete time delay systems. Analyzing the finite time stability concept, these new delay-independent conditions are derived using an approach based on the Lyapunov-like functions. The practical and attractive practical stability for discrete time delay systems has been investigated. The above mentioned approach was supported by the classical Lyapunov technique to guarantee the attractivity properties of the system behavior.

Novel conditions for finite time stability of discrete time delay systems

2013 International Conference on System Science and Engineering (ICSSE), 2013

In this article novel sufficient conditions for the practical and finite time stability of linear continuous system with time delay have been presented. A general mathematical description of the systems investigated was given as x(k+1)=A 0 x(k) + A 1 x(k-h). The proposed approach was based on the investigation of the Lyapunov-like functions which was used for derivation of the novel stability conditions, independent of time delay. The obtained results were applied to the investigation of systems' stability. The basic advantages of the presented conditions were the following: the functions used here did not have to be positive on the state space and there was no need for negative derivatives along the trajectory of systems.

Further results on stability of linear discrete time delay systems over a finite time interval: Novel delay-independent conditions

2011 9th IEEE International Conference on Control and Automation (ICCA), 2011

ABSTRACT This paper gives sufficient conditions for the practical and finite time stability of a particular class of linear discrete time delay systems. Analyzing the finite time stability concept, these new delay-independent conditions are derived using an approach based on the Lyapunov-like functions. The practical stability and attractive practical stability for discrete time delay systems have been investigated. The above mentioned approach was supported by the classical Lyapunov technique to guarantee the attractivity properties of the system behavior.

Finite-time stability criteria of linear system with non-differentiable time-varying delay via new integral inequality

2020

In this article, a new integral inequality based on a free-matrix for bounding the integral ∫ a b x T ( u ) R x ( u ) d u has been proposed. The new inequality and appropriated Lyapunov–Krasovskii functional play key roles for deriving finite-time stability criteria of linear systems with constant and continuous non-differentiable time-varying delays. The new sufficient finite-time stability conditions have been proposed in the forms of inequalities and linear matrix inequalities. In addition, we apply the same procedure as done for deriving finite-time stable criteria but using Wirtinger-based inequality instead of our new inequality and compare these criteria with other works. At the end, two numerical examples are presented to show that the proposed criteria are practicable for linear systems with non-differentiable delay. Criteria using proposed integral inequality yield better results than the other works for linear system with constant delay. However, results using Wirtinger i...

Further Results on Finite Timeand Practical Stability of Linear Continuous Time Delay Systems

In this paper, finite-time stability and practical stability problems for a class of linear continuous time-delay systems are studied. Based on the Lyapunov-like functions, that do not have to be positive definite in the whole state space and not need to have negative definite derivatives along the system trajectories, the new sufficient finite-time stability conditions are obtained. To obtain the conditions for attractive practical stability, the mentioned approach is combined with classical Lyapunov technique to guarantee attractivity properties of system behavior, and new delay dependent sufficient condition has been derived. The described approach was compared with some previous methods and it has been showed that the results derived are commonly adequate but easier for numerical treatment.

Finite time stability of continuous time delay systems: Jensen's inequality-based approach

2014 9th IEEE Conference on Industrial Electronics and Applications, 2014

In this study, finite-time stability of the linear continuous time-delay systems was investigated. A novel formulation of the Lyapunov-like function was used to develop a new sufficient delay-dependent condition for finite-time stability. The proposed function does not need to be positive-definite in the whole state space, and it does not need to have negative derivatives along the system trajectories. The proposed method was compared with the previously developed and reported methodologies. It was concluded that the stability investigation using the novel condition for stability investigation was less complicated for numerical calculations. Furthermore, it gives comparable results in comparison with the ones obtained with other analyzed conditions, and it provides superior results for some systems.

An efficient method for finite time stability calculation of continuous time delay systems

2013 9th Asian Control Conference (ASCC), 2013

This paper provides sufficient conditions for the finite time stability of linear continuous time delay systems mathematically described as x , (t)=A 0 x(t) + A 1 x(t-τ). A novel method was used to derive new delay dependent conditions. The conditions obtained were applied in the system stability analysis. Consequently, the aggregation function does not have to be positive in the state space domain, and does not need to have the negative derivatives along the system trajectories. Finite time stability was analyzed using the novel conditions derived in the paper. The described approach was compared with some known methods. It was proved that the new results were in compliance with the previously reported results, but more convenient for numerical calculations. The numerical example was presented to support the results.

Finite Time Stability of Linear Control Systems with Multiple Delays

s In this paper, we considered finite time stability of a class of linear control systems. By using suitable matrix measures and Coppel's inequality a bound for the solution of the linear control system with multiple delays in the state is determined. A sufficient delay dependent conditions for finite time stability of linear control system with delay are derived.

Delay-Dependent Conditions for Finite Time Stability of Continuous Systems with Latency

2013

In the present study, the practical and finite time stability of linear continuous system with latency has been investigated. The proposed result outlines the novel sufficient stability conditions for the systems represented by the following equation: x(t)=A 0 x(t) -A 1 x(t -). The results can be applied to the analysis of both the practical and finite time stability of the continuous systems with time delay. For the derivation of the finite time stability conditions, the Lyapunov-Krassovski functionals were used. Unlike in the previously reported results, the functionals did not have to satisfy some strict mathematical conditions, such as positivity in the whole state space and possession of the negative derivatives along the system state trajectories. The numerical examples presented in this study additionally clarified the implementation of the methodology, and the calculations of the stability conditions. Generally, it was found that the proposed sufficient conditions were less restrictive compared to the ones previously reported.