What is the State Space Analysis?
State Space Analysis is the graphical tool that is used to analyze and design the linear, non-linear, time-variant, time-invariant multi-input, multi-output system. It is used to describe the behavior of LTI systems. It describes the internal state of the system. There are various key components of the state space analysis which are as follows:
- State and State Variable
- State Vector
- State Space
State and State Variable
The state of a dynamical system is a set of minimal variables and the knowledge of these variables at t=to together with input for [Tex]t\geq t_{o} [/Tex] completely determines the behavior of the system for any time t. In other words, the compact representation of the previous history of the system is known as the State of the system.
The variables that contain the dynamic information of the system are known as State Variables.
State Vector
The ‘n’ set of state variables which describes the dynamic equations of the linear system, then it can be considered as N components of a vector q. The given below is the state vector of continuous system.
State Vector
State Space
When the coordinate axis of the N-dimensional space consist of q1-axis, q2-axis, …., qn-axis, it is known as state space. Any state can be represented by the point in the state space.
What is State Space Analysis ?
The State Space analysis applies to the non-linear and time-variant system. It helps in the analysis and design of linear, non-linear, multi-input, and multi-output systems. Earlier the transfer function applied to the linear time-invariant system but with the help of State Space analysis, it is possible to find the transfer function of the non-linear and time-variant systems. In this article, we will study the State Space Model in control system engineering.
Table of Content
- What is the State Space Analysis?
- State Space Model
- Transfer Function from State Space Model
- State Transition Matrix and its Properties
- Controllability and Observability
- Solved Example on State Space Analysis
- Advantages and Disadvantages of State Space Analysis
- Applications of State Space Analysis