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Chapter 7: Q1E (page 380)

For the matrices A in Exercises 1 through 10 , determine whether the zero state is a stable equilibriunt of the dynamical system x鈫�(i+1)=Ax鈫�(i)

1.A=[0.9000.8],

Short Answer

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Stable

Step by step solution

01

Determine whether the zero state is a stable equilibriunt

The matrix A is diagonal, so we have

At=[0.9t000.8t],Atx0=[0.9t000.8t][x1x2]=[0.9tx1000.8tx2],

Which leads to

limt鈫�鈭�Atx0=0,x0鈭�鈩�2.

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Most popular questions from this chapter

Find all the polynomials of degree 鈮�2[a polynomial of the formf(t)=a+bt+ct2] whose graph goes through the points (1,3) and (2,6) , such thatrole="math" localid="1659541039431" f'(1)=1[wheref'(1)denotes the derivative].

Prove the part of Theorem 7.2.8 that concerns the trace: If an n 脳 n matrix A has n eigenvalues 位1, . . . , 位n, listed with their algebraic multiplicities, then tr A = 位1+路 路 路+位n.

If v鈬赌is any nonzero vector in R2 , what is the dimension of the space Vof all 2脳2matrices for which v鈬赌is an eigenvector?

For which2脳2 matrices A does there exist a nonzero matrix M Such that AM=MD,whereD=[2003] Give your answer in terms of eigenvalues of A.

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[010001100]
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