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Digital Control
Systems
State Space Analysis(1)
Control
Systems
Space Analysis(1)
Page 2


Digital Control
Systems
State Space Analysis(1)
Control
Systems
Space Analysis(1)
INTRODUCTION
Page 3


Digital Control
Systems
State Space Analysis(1)
Control
Systems
Space Analysis(1)
INTRODUCTION INTRODUCTION
State space: The n-dimensional space whose coordinate axes consist of
axis  is called a state space.
State-space equations: In state-space analysis, we are concerned with
that are involved in the modeling of dynamic systems: input
state variables.
For Linear or Nonlinear discrete-time systems:
dimensional space whose coordinate axes consist ofthex
1
-axis, x
2
-axis,..x
n
-
space analysis, we are concerned with three types of variables
that are involved in the modeling of dynamic systems: input variables, output variables, and
Page 4


Digital Control
Systems
State Space Analysis(1)
Control
Systems
Space Analysis(1)
INTRODUCTION INTRODUCTION
State space: The n-dimensional space whose coordinate axes consist of
axis  is called a state space.
State-space equations: In state-space analysis, we are concerned with
that are involved in the modeling of dynamic systems: input
state variables.
For Linear or Nonlinear discrete-time systems:
dimensional space whose coordinate axes consist ofthex
1
-axis, x
2
-axis,..x
n
-
space analysis, we are concerned with three types of variables
that are involved in the modeling of dynamic systems: input variables, output variables, and
INTRODUCTION
For Linear Time-varying discrete-time systems:
Page 5


Digital Control
Systems
State Space Analysis(1)
Control
Systems
Space Analysis(1)
INTRODUCTION INTRODUCTION
State space: The n-dimensional space whose coordinate axes consist of
axis  is called a state space.
State-space equations: In state-space analysis, we are concerned with
that are involved in the modeling of dynamic systems: input
state variables.
For Linear or Nonlinear discrete-time systems:
dimensional space whose coordinate axes consist ofthex
1
-axis, x
2
-axis,..x
n
-
space analysis, we are concerned with three types of variables
that are involved in the modeling of dynamic systems: input variables, output variables, and
INTRODUCTION
For Linear Time-varying discrete-time systems:
INTRODUCTION
For Linear Time-invariant discrete-time systems systems:
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FAQs on PPT - Discrete state space model - Electrical Engineering (EE)

1. What is a discrete state space model?
Ans. A discrete state space model is a mathematical representation of a system that can be described by a finite number of distinct states. It is commonly used in various fields such as control systems, computer science, and economics to analyze and predict the behavior of a system over time.
2. How is a discrete state space model different from a continuous state space model?
Ans. A discrete state space model represents a system that can only occupy a finite number of states, whereas a continuous state space model represents a system that can occupy an infinite number of states. In a discrete state space model, the system transitions from one state to another at specific time points, while in a continuous state space model, the system transitions smoothly between states over a continuous range of time.
3. What are the advantages of using a discrete state space model?
Ans. Using a discrete state space model offers several advantages. Firstly, it simplifies the analysis and prediction of system behavior by reducing the complexity of continuous systems to a finite number of states. Secondly, it allows for the use of discrete-time techniques, which are often easier to implement and analyze than continuous-time techniques. Lastly, discrete state space models are computationally efficient and can be easily simulated and tested.
4. How are state transitions represented in a discrete state space model?
Ans. In a discrete state space model, state transitions are typically represented using a transition matrix. This matrix defines the probabilities of transitioning from one state to another. Each row of the matrix represents the probabilities of transitioning from a specific state to all possible states. By multiplying the transition matrix with the initial state vector, the future state of the system can be predicted.
5. What are some real-world applications of discrete state space models?
Ans. Discrete state space models have various real-world applications. For example, they are widely used in finance to model stock prices and predict market trends. In robotics, discrete state space models are used to control the movements of robots based on their current state and desired objectives. Additionally, discrete state space models are utilized in healthcare to model the progression of diseases and predict patient outcomes.
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