Since eAt 1 si A1 we might argue that eAt 1 si A Is this t

Since e^At =^-1 ((si - A)^-1), we might argue that e^-At =^-1 ((si - A)). Is this true or false? Explain.

Solution

FALSE

(sI A ) ¹ is called the resolvent of A.

The state-transition matrix is L¹ (sI A)¹ = e^tA

^So, L¹(sI A ) ¹ is not equal to (L¹(sI-A))1