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Chapter 7: Q6E (page 380)

Use eigenvalues to determine the stability of a dynamical system. Analyse the dynamical systemx鈫�(t+1)=Ax鈫�(t), where A is a real2脳2matrix with eigenvaluep卤iqFor the matrices A in Exercises 1 through 10, determine whether the zero state is a stable equilibrium of the dynamical system.x鈫�(t+1)=Ax鈫�(t)

A=[13-1.22.6]

Short Answer

Expert verified

The stability of the dynamical systemusing eigenvalues is Unstable.

Step by step solution

01

solve the given matrix by eigenvalues:

Use the characteristic equation

det(A鈭�位I)=0|鈭�1鈭�位3鈭�1.22.6鈭�位|=0(鈭�1鈭�位)(2.6鈭�位)+3.6=0

位2鈭�1.6位+1=0位1,2=1.6卤2.56鈭�42=0.8卤0.6i

Since|位1|=|位2|=1 then, the equilibrium is unstable

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Most popular questions from this chapter

22: Consider an arbitrary n 脳 n matrix A. What is the relationship between the characteristic polynomials of A and AT ? What does your answer tell you about the eigenvalues of A and AT ?

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0-112
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