Delay-independent Stability of Uncertain Control Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 277-283 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Mehdi Ahmadian
Keyword(s):  
Control Systems ◽  
Uncertain Systems ◽  
Extreme Values ◽  
Sufficient Conditions ◽  
Entire Family ◽  
Active Vibration ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Analytical Expressions

This paper will provide a study of the delay-independent stability of uncertain control systems, represented by a family of quasipolynomials with single time-delays. The uncertain systems that are considered here are delay differential systems whose parameters are known only by their lower and upper bounds. The results are given in the form of necessary and sufficient conditions along with the assumptions for the quasipolynomial families considered. The conditions are transformed into convenient forms, which provide analytical expressions that can be easily checked by commercially available computing tools. For uncertain systems represented by families of quasipolynomials, it is shown that the delay independent stability for the extreme values of parameters is not sufficient for the delay independent stability of the entire family. In addition, the family must satisfy some conditions for the interior values of each parameter within specially constructed frequency ranges. The implementation of the theorem that is suggested is demonstrated on an example system that includes a single degree of freedom system with an active vibration absorber, namely the Delayed Resonator.

scholarly journals Second-Order Impulsive Delay Differential Systems: Necessary and Sufficient Conditions for Oscillatory or Asymptotic Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 722
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz ◽  
Ali Muhib ◽  
Shao-Wen Yao
Keyword(s):  
Asymptotic Behavior ◽  
Differential System ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Impulsive Delay ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient

In this work, we aimed to obtain sufficient and necessary conditions for the oscillatory or asymptotic behavior of an impulsive differential system. It is easy to notice that most works that study the oscillation are concerned only with sufficient conditions and without impulses, so our results extend and complement previous results in the literature. Further, we provide two examples to illustrate the main results.

scholarly journals Persistence and Stability for a Class of Forced Positive Nonlinear Delay-Differential Systems

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
D. Franco ◽  
C. Guiver ◽  
H. Logemann
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Breeding Programmes ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay ◽  
Stability Concept

AbstractPersistence and stability properties are considered for a class of forced positive nonlinear delay-differential systems which arise in mathematical ecology and other applied contexts. The inclusion of forcing incorporates the effects of control actions (such as harvesting or breeding programmes in an ecological setting), disturbances induced by seasonal or environmental variation, or migration. We provide necessary and sufficient conditions under which the states of these models are semi-globally persistent, uniformly with respect to the initial conditions and forcing terms. Under mild assumptions, the model under consideration naturally admits two steady states (equilibria) when unforced: the origin and a unique non-zero steady state. We present sufficient conditions for the non-zero steady state to be stable in a sense which is reminiscent of input-to-state stability, a stability notion for forced systems developed in control theory. In the absence of forcing, our input-to-sate stability concept is identical to semi-global exponential stability.

SCALED AND SCALING-FREE McCLELLAN TRANSFORMATIONS FOR THE DESIGN OF 2-D DIGITAL FILTERS

1991 ◽  
Vol 01 (01) ◽  
pp. 105-124 ◽  
Author(s):  
N. NAGAMUTHU ◽  
M. N. S. SWAMY
Keyword(s):  
Real Time ◽  
Digital Filters ◽  
Extreme Values ◽  
Sufficient Conditions ◽  
Scaling Factors ◽  
Mcclellan Transformation ◽  
Real Time Applications ◽  
Necessary And Sufficient ◽  
New Formula ◽  
Analytical Expressions

In this paper, the scaling problem of McClellan transformation used for the design 2-D digital filters with elliptical and circular cutoff contours is critically analyzed. Several new and extremely simple formulas for calculating the maximum and minimum values of the transformation function are presented. Using these extreme values, simple formulas for scaling factors and scaled McClellan transformations are derived for the various cases of each type of contour. Using the necessary and sufficient conditions for a scaling-free transformation, the scaling-free McClellan transformations are also derived. It is shown that the number of independent coefficients in them to be optimized varies from 0 to 2 depending on the case, compared to 3 in the original transformation. They are very useful in deriving analytical expressions for the transformation coefficients, and the 2-D filters designed by employing them have a smaller number of multiplications per output sample and hence, attractive for real-time applications. A new scaling formula is presented and some of its properties and effects on the derived formulas are discussed. The major advantage of this new formula is that from the unscaled transformation coefficients for a given type of 2-D filter, we can generate the scaled transformation coefficients for a different type of 2-D filter. Some examples are presented to demonstrate the usefulness of the derived formulas.

Oscillation of the Riemann–Weber Version of Euler Differential Equations with Delay

2000 ◽  
Vol 7 (3) ◽  
pp. 577-584
Author(s):  
Jitsuro Sugie ◽  
Mitsuru Iwasaki
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Equations With Delay ◽  
Oscillation Of Solutions

Abstract Our concern is to consider delay differential equations of Euler type. Necessary and sufficient conditions for the oscillation of solutions are given. The results extend some famous facts about Euler differential equations without delay.

Robust Stability of Sequential Multi-input Multi-output Quantitative Feedback Theory Designs

2004 ◽  
Vol 127 (2) ◽  
pp. 250-256 ◽  
Author(s):  
Murray L. Kerr ◽  
Suhada Jayasuriya ◽  
Samuel F. Asokanthan
Keyword(s):  
Control Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Internal Stability ◽  
Quantitative Feedback Theory ◽  
Recursive Design ◽  
Stability Theorems ◽  
Improved Design ◽  
The Stability ◽  
Necessary And Sufficient

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

Finite time stability of semilinear multi-delay differential systems

2017 ◽  
Vol 40 (9) ◽  
pp. 2948-2959
Author(s):  
JinRong Wang ◽  
Zijian Luo
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Differential Systems ◽  
Finite Time Stability ◽  
Alternative Approach ◽  
Representation Of Solutions ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Exponential Matrix

In this paper, we provide an alternative approach to study finite time stability for semilinear multi-delay differential systems with pairwise permutable matrices associated with the stand and generalized Landau symbol conditions for nonlinear terms. The explicit representation of solutions involving a special multi-delayed exponential matrix function is developed to establish sufficient conditions to guarantee the systems are finite time stable by virtue of Gronwall integral inequalities with delay. Finally, we demonstrate the validity of the designed method and discuss it using numerical examples.

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