Which of the following functions V: R →RI a Lyapunov function for the respective continuous-time system? In each case, we consider the compact invariant set I = {0}. V(x) = 2,ż = -z?. V (x) = r³,ż = -z. V (2) = a, ż = -z. V(z) = r°,ż = -r?.

Which of the following functions V: R →RI a Lyapunov function for the respective continuous-time system? In each case, we consider the compact invariant set I = {0}. V(x) = 2,ż = -z?. V (x) = r³,ż = -z. V (2) = a, ż = -z. V(z) = r°,ż = -r?.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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Question

Which of the following functions V: R → Ris a Lyapunov function for the respective continuous-time system? In each case, we consider the compact
invariant set I = {0}.
V(x) = 2³,ż = -2?.
V(x)= x³,ż = -z.
V (x) = x², ż = -r.
V(z) = x°,ż = -x?.

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