linear system by Meiling CHEN1 Lesson 6 State transition matrix Linear system 1. Analysis

linear system by Meiling CHEN2 1.Homogeneous solution of x(t) 2.Non-homogeneous solution of x(t) The behavior of x(t) et y(t) :

linear system by Meiling CHEN3 Homogeneous solution State transition matrix

linear system by Meiling CHEN4 Properties

linear system by Meiling CHEN5 Non-homogeneous solution Convolution Homogeneous

linear system by Meiling CHEN6 Zero-input responseZero-state response

linear system by Meiling CHEN7 Example 1 Ans:

linear system by Meiling CHEN8 Using Maison’s gain formula

linear system by Meiling CHEN9 How to findState transition matrix Methode 1: Methode 3: Cayley-Hamilton Theorem Methode 2:

linear system by Meiling CHEN10 Methode 1:

linear system by Meiling CHEN11 Methode 2: diagonal matrix

linear system by Meiling CHEN12 Diagonization

linear system by Meiling CHEN13 Diagonization

linear system by Meiling CHEN14 Case 1: depend

linear system by Meiling CHEN15 In the case of A matrix is phase-variable form and Vandermonde matrix for phase-variable form

linear system by Meiling CHEN16 Case 1: depend

linear system by Meiling CHEN17

linear system by Meiling CHEN18 Case 3:Jordan form Generalized eigenvectors

linear system by Meiling CHEN19 Example:

linear system by Meiling CHEN20 Method 3:

linear system by Meiling CHEN21 any

linear system by Meiling CHEN22 Example:

linear system by Meiling CHEN23 Example:

linear system by Meiling CHEN24

linear system by Meiling CHEN25

linear system by Meiling CHEN26

linear system by Meiling CHEN27

linear system by Meiling CHEN28

linear system by Meiling CHEN29