Linear system 1 Analysis Lesson 6 State transition

Linear system 1. Analysis Lesson 6 State transition matrix linear system by Meiling CHEN 1

The behavior of x(t) et y(t) : 1. Homogeneous solution of x(t) 2. Non-homogeneous solution of x(t) linear system by Meiling CHEN 2

Homogeneous solution State transition matrix linear system by Meiling CHEN 3

Properties linear system by Meiling CHEN 4

Non-homogeneous solution Convolution Homogeneous linear system by Meiling CHEN 5

Zero-input response Zero-state response linear system by Meiling CHEN 6

Example 1 Ans: linear system by Meiling CHEN 7

Using Maison’s gain formula linear system by Meiling CHEN 8

How to find State transition matrix Methode 1: Methode 2: Methode 3: Cayley-Hamilton Theorem linear system by Meiling CHEN 9

Methode 1: linear system by Meiling CHEN 10

Methode 2: diagonal matrix linear system by Meiling CHEN 11

Diagonization linear system by Meiling CHEN 12

Diagonization linear system by Meiling CHEN 13

Case 1: depend linear system by Meiling CHEN 14

In the case of A matrix is phase-variable form and Vandermonde matrix for phase-variable form linear system by Meiling CHEN 15

Case 1: depend linear system by Meiling CHEN 16

linear system by Meiling CHEN 17

Case 3: Jordan form Generalized eigenvectors linear system by Meiling CHEN 18

Example: linear system by Meiling CHEN 19

Method 3: linear system by Meiling CHEN 20

any linear system by Meiling CHEN 21

Example: linear system by Meiling CHEN 22

Example: linear system by Meiling CHEN 23

linear system by Meiling CHEN 24

linear system by Meiling CHEN 25

linear system by Meiling CHEN 26

linear system by Meiling CHEN 27

linear system by Meiling CHEN 28

linear system by Meiling CHEN 29