Example to Calculate State Transition Matrix
Question
Calculate the state transition matrix where system matrix is given as ,
A=
Solution
System matrix A=
Given A=
Where
Ф(s)=
where matrix=[sI-A]
det(matrix)=s(s+3)-(-2)
=
det(matrix)=(s+2)(s+1)
Ф(s)=
Ф(s)=
Ф(t)= { Ф(s) }=
Important Properties of State Transition Matrix
A state transition matrix is a fundamental concept used to describe the Fundamental evolution of a linear time-invariant system in a state space representation. The state transition matrix is often represented by Ф(t). In this article, we will Go Through What is State Transition Matrix, What is Linear time-invariant System, the General Representation State Transition Matrix, and the Mathematical expression for the state transition matrix, and At last we will go through Solved examples of State Transition Matrix with its Application, Advantages, Disadvantages, and FAQs.
Table of Content
- State Transition Matrix
- LTI System
- General Representation
- Mathematical expression
- Steps to evaluate
- Example
- Properties
- Advantages
- Disadvantages
- Applications
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