scholarly journals Stability of Ulam–Hyers and Existence of Solutions for Impulsive Time-Delay Semi-Linear Systems with Non-Permutable Matrices

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1493
Author(s):  
Nazim I. Mahmudov ◽  
Amal M. Almatarneh
Keyword(s):  
Time Delay ◽  
Existence Of Solutions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Representation Formula ◽  
Matrix Exponential ◽  
Delay Systems ◽  
Impulsive Systems ◽  
Impulsive Delay ◽  
The Stability

In this paper, the stability of Ulam–Hyers and existence of solutions for semi-linear time-delay systems with linear impulsive conditions are studied. The linear parts of the impulsive systems are defined by non-permutable matrices. To obtain solution for linear impulsive delay systems with non-permutable matrices in explicit form, a new concept of impulsive delayed matrix exponential is introduced. Using the representation formula and norm estimation of the impulsive delayed matrix exponential, sufficient conditions for stability of Ulam–Hyers and existence of solutions are obtained.

scholarly journals Stochastic stability of linear time-delay system with Markovian jumping parameters

1997 ◽  
Vol 3 (3) ◽  
pp. 187-201 ◽  
Author(s):  
K. Benjelloun ◽  
E. K. Boukas
Keyword(s):  
Time Delay ◽  
Stochastic Stability ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay System ◽  
Delay Systems ◽  
Necessary Condition ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
The Stability

This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP). We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.

Robust Stabilizability of Uncertain Linear Time-Delay Systems With Markovian Jumping Parameters

1996 ◽  
Vol 118 (4) ◽  
pp. 776-783 ◽  
Author(s):  
K. Benjelloun ◽  
E. K. Boukas ◽  
H. Yang
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Linear Type ◽  
Continuous State ◽  
The Stability

In this paper, we deal with the robust stabilizability of the class of uncertain linear time-delay systems with Markovian jumping parameters and unknown but bounded uncertainties. Under the assumption of the complete access to the continuous state, the stochastic controllability of the nominal system and the boundedness of the system’s uncertainties, sufficient conditions which guarantee the robustness of the stability of this class of systems are given. The control law which guarantees the robustness of the stabilizability is linear-type or saturation-type. An example is presented to illustrate the usefulness of the proposed theoretical results.

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

The Stability Analysis and Planning for Multivariable Linear Time-Delay Systems and its Application in Supervision Oilfield

2013 ◽  
Vol 709 ◽  
pp. 727-730
Author(s):  
Ren Wang ◽  
Xue Kun Qi ◽  
Long Xing
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Linear Time ◽  
Control Process ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Water Separation ◽  
Delayed Systems ◽  
Delayed System ◽  
The Stability

Based on Lyapunovs theory of stability, analyze on a control process of oil-water separation with time-delay, coupling and uncertainty in the unite station. a equation of sufficient condition for multi-variable Linear Delayed Systems with delayed independent stabilization is derived and another forms are also given. Based on this, several simple criterions for judging independent stabilization from linear delayed system are presented. We also discuss the exponential stability for delayed system and also provide the sufficient condition of exponential stability with any appointed convergent rate and its corresponding deductions. Using these conditions, we can choose a set of suitable parameters to reduce the conservation. By calculating and being compared with methods of the literature, the results show that our methods have less conservation.

scholarly journals Delay dependent stability of linear time-delay systems

2013 ◽  
Vol 40 (2) ◽  
pp. 223-245 ◽  
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic
Keyword(s):  
Time Delay ◽  
Large Scale ◽  
Linear Time ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Lyapunov Equation ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with the problem of delay dependent stability for both ordinary and large-scale time-delay systems. Some necessary and sufficient conditions for delay-dependent asymptotic stability of continuous and discrete linear time-delay systems are derived. These results have been extended to the large-scale time-delay systems covering the cases of two and multiple existing subsystems. The delay-dependent criteria are derived by Lyapunov's direct method and are exclusively based on the solvents of particular matrix equation and Lyapunov equation for non-delay systems. Obtained stability conditions do not possess conservatism. Numerical examples have been worked out to show the applicability of results derived.

scholarly journals Feedback control of time-delay systems with bounded control and state

1995 ◽  
Vol 1 (1) ◽  
pp. 77-87 ◽  
Author(s):  
M. Dambrine ◽  
J. P. Richard ◽  
P. Borne
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Linear Constraints ◽  
State Feedback Control ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Bounded Control ◽  
Controlled Systems

This paper is concerned with the problem of stabilizing linear time-delay systems under state and control linear constraints. For this, necessary and sufficient conditions for a given non-symmetrical polyhedral set to be positively invariant are obtained. Then existence conditions of linear state feedback control law respecting the constraints are established, and a procedure is given in order to calculate such a controller. The paper concerns memoryless controlled systems but the results can be applied to cases of delayed controlled systems. An example is given.

Efficient Computation of Stability Charts for Linear Time Delay Systems

2005 ◽  
Author(s):  
Dimitri Breda ◽  
Stefano Maset ◽  
Rossana Vermiglio
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Computational Cost ◽  
Characteristic Root ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Efficient Computation ◽  
Square Grid ◽  
Stability Chart ◽  
The Stability

A new efficient algorithm for the computation of the stability chart of linear time delay systems is proposed and tested on several examples. The stability chart is obtained by investigating the 2d-parameter space by a first coarse square grid which is then adaptively refined by triangulation to match the desired tolerance. This leads to a considerable reduction in computational cost with respect to investigate a uniform fine square grid. Stability of each point is determined by approximating the rightmost characteristic root real part via a numerical scheme recently developed by the authors and based on pseudospectral differencing methods. A Matlab code is included in appendix.

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