Numerical Solution for Linear State Space Systems using Haar Wavelets Method

Waleeda Swaidan Ali,Haleema S Ali

doi:10.21123/bsj.2022.19.1.0084

Abstract

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

Highlights

A state space is a mathematical model of a physical system, with involving a set of state variables interrelated by first order differential equations with zero initial conditions 1
The Haar wavelet basis function and Haar wavelet operational matrix are interested to approximate a system of differential equations
The formulates of the Haar wavelet method and Haar operational matrix are presented in the third part of this paper

Summary

Introduction

A state space is a mathematical model of a physical system, with involving a set of state variables interrelated by first order differential equations with zero initial conditions 1. The Haar wavelet basis function and Haar wavelet operational matrix are interested to approximate a system of differential equations. Based on Haar wavelet method, Prabakaran et al used Haar wavelet series method to get discrete solutions for a state space system of differential equations. Karimi et al solved second-order linear systems with respect to a quadratic cost function using Haar wavelet. Haar wavelet operational matrix of integration and Haar wavelet collocation points with the operation vec for one dimension on the interval. The formulates of the Haar wavelet method and Haar operational matrix are presented in the third part of this paper. The proposed strategy to approximate the linear state space system by using Haar operational matrix, and Haar wavelet collocation points are presented. Where x(t) R n1 is a vector of state space, A is n1 n1the system matrix, B is the constant vector n1 1and x(0) x0 is the initial condition vector of size n1 1

Haar wavelets

This equation can be rewritten into compact form as

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