Evaluation of Costate Variables and Performance Index to the Feedback Path for a Time Varying System by Norm Linear Bounded Linear Differential Inclusions Method

2020 ◽  
pp. 845-852
Author(s):  
Nirmalya Chandra ◽  
Achintya Das
Keyword(s):  
Performance Index ◽  
Differential Inclusions ◽  
Time Varying ◽  
Bounded Linear ◽  
Feedback Path ◽  
Linear Differential Inclusions ◽  
Linear Differential ◽  
And Performance

scholarly journals Quadratic Stability of Non-Linear Systems Modeled with Norm Bounded Linear Differential Inclusions

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1432
Author(s):  
Mutti-Ur Rehman ◽  
Jehad Alzabut ◽  
Arfan Hyder
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusions ◽  
Bounded Linear ◽  
Linear Dynamical Systems ◽  
Quadratic Stability ◽  
Linear Differential Inclusions ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability ◽  
Non Linear System

In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed methodology reformulate non-linear differential inclusion to an equivalent non-linear system. Lyapunov function demonstrate the existence of a symmetric positive definite matrix to analyze the stability of non-linear dynamical systems. The proposed method allows us to construct a system of ordinary differential equations to localize the spectrum of perturbed system which guarantees the stability of non-linear dynamical system.

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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