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Chapter 7: Q7.6-30E (page 381)

Consider an invertible n 脳 n matrix A such that the zero state is a stable equilibrium of the dynamical systemx鈫�(t+1)=Ax鈫�(t).What can you say about the stability of the systems

x鈫�(t+1)=A2x鈫�(t)

Short Answer

Expert verified

The given system is stable

Step by step solution

01

Define eigenvalue

Eigenvalues can be used to determine whether a fixed point (also known as an equilibrium point) is stable or unstable.

02

To the stability of the given system

limt鈫�鈭�A2tx0=limt鈫�鈭�A2tx0=0

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Most popular questions from this chapter

Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformations in Exercises 15 through 22. In each case, find an eigenbasis if you can, and thus determine whether the given transformation is diagonalizable.

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