Stability Analysis Of Discrete Time-varying Linear Systems Based On SVD Decomposition

Moment is a vital image processing and analysis tool,which has been widely used in computer technology,image retrieval,pattern recognition and other fields.Based on orthogonal polynomial,functions of the numerical stability of Orthogonal moment will be changed by the increase of The order of moments and Calculation of accumulation speed,which caused by the instability in the process of calculation,then it will affect the effect of image reconstruction,and at this stage need to be calculated by means of orthogonal moment numerical divergence sex to provide identification method for pattern recognition,and the ability to refactor even multidimensional goal for the image of the higher order moment of precise calculation provide effective technical support.However,due to the complex analytic formula of orthogonal polynomials,it is generally used to solve polynomial values in the practical application.Fu,W.G autschi wait for second order recursive computation problem have done a lot of meaningful exploration,discussed the recursive discrete orthogonal polynomial convergence,but failed to find the second order recursive system numerical stability of the effective methods to determine.The stability of the second-order discrete linear time-varying system is studied extensively,but there are still some limitations.For these problems,this paper studies the stability of discrete time-varying linear systems.The main research contents are as follows:1.This paper firstly gives the definition of the continuous orthogonal matrix and discrete orthogonal moment,also the recursive formula of classical orthogonal polynomial is given.Based on the second-order discrete time-varying linear system theory,we transforms the Three recursion formulas into Order number to discuss order differential equation,then to discuss the stability of recursive system,and analyzes the error condition.2.Based on the lyapunov theorem,a state matrix is decomposed into multiplication of a unitary matrix with a diagonal matrix and a unitary matrix.Through the analysis of the second order discrete time-varying system stability by using SVD decomposition,turning it into the RS system(a unit of rotation matrix R,a tensile matrix S).The criterion of divergence and convergence of the first quadrant,divergence of the second quadrant and divergence of quadrants are given.In this paper,Recursive formula of Tchebichef orthogonal polynomials,Recursive formula of Tchebichef deformed orthogonal polynomials and the recursion of the orthogonal polynomial of Jacobsthal and Krawtchouk are simulated in Matlab to do Divergent trajectories.3.Through Matlab simulation,calculates including the series changes in different angles,the size of the singular value changes,the changes of amplitude ratio and slope of the Tchebichef polynomial,polynomial Tchebichef deformation,Krawtchouk polynomial,Jacobsthal polynomial.The criterion of divergence and convergence of the first quadrant,divergence of the second quadrant and divergence of the second-fourth quadrant are verified.4.Because orthogonal moment in image reconstruction,image retrieval,image analysis has been widely used,so the author uses Tchebichef polynomial,Tchebichef deformation,Krawtchouk polynomial of a polynomial is reconstructed 256 gray image 400 x 400,has proved its application in image reconstruction.