Systems of linear differential equations with $ \pi$-derivative and linear differential inclusions

2005 ◽  
Vol 196 (11) ◽  
pp. 1677-1691 ◽  
Author(s):  
N V Plotnikova
Keyword(s):  
Differential Equations ◽  
Differential Inclusions ◽  
Linear Differential Equations ◽  
Linear Differential Inclusions ◽  
Linear Differential

scholarly journals Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 152
Author(s):  
Mutti-Ur Rehman ◽  
Sohail Iqbal ◽  
Jehad Alzabut ◽  
Rami Ahmad El-Nabulsi
Keyword(s):  
Differential Equations ◽  
Differential Inclusions ◽  
Linear Time ◽  
System Of Differential Equations ◽  
Bounded Linear ◽  
Linear Time Invariant ◽  
Linear Differential Inclusions ◽  
Linear Time Invariant Systems ◽  
Linear Differential ◽  
Time Invariant

In this article, we present a stability analysis of linear time-invariant systems in control theory. The linear time-invariant systems under consideration involve the diagonal norm bounded linear differential inclusions. We propose a methodology based on low-rank ordinary differential equations. We construct an equivalent time-invariant system (linear) and use it to acquire an optimization problem whose solutions are given in terms of a system of differential equations. An iterative method is then used to solve the system of differential equations. The stability of linear time-invariant systems with diagonal norm bounded differential inclusion is studied by analyzing the Spectrum of equivalent systems.

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