In this section, we will examine **UNIT 04 STATE VARIABLE ANALYSIS | Basic Signal and Systems -AKTU**, **subject “Electrical and Electronics Engineering”**. I hope this article is useful to you as you prepare for your AKTU exams.

Dudes 🤔.. You want more useful details regarding this subject. Please keep in mind this as well.Important Questions For Basic Signals and Systems :*Unit-01 *Unit-02 *Unit-03 *Unit-04 *Unit-05 *Short-Q/Ans *Question-Paper with solution 21-22

**Q1. What is state variable analysis ? Also define state and state variable. **

**Ans. ****A. State variable analysis :** It is best to construct a set of n first-order differential equation using a set of auxiliary variables called state variables, and this method is known as State Variable Analysis. An n^{th} order differential equation is typically not suitable for computer solution.

**B. Definition of the following terms: **

**i. State: **The state of a dynamic system is the smallest set of variables such that the knowledge of these variables att = t_{0} with the of knowledge the input for t ≥ t, completely determines the behaviour of the system for any time t ≥ t_{0}.

**ii. State variables: **State variables are the factors that contribute to the dynamical system’s determination of its state.

**iii. State vector:** These n state variables may be regarded as n components of a vector x if n variables are required to fully characterize the behaviour of a particular system. State vector refers to such a vector.

i**v. State space:**** **The n-dimensional space whose coordinate axes consists of the x_{1} axis, x_{2} axis…..,x_{n} axis is called state space. Any state can be represented by a point in the state space.

**v. State equation:** A state space representation, also known as a state equation, is a mathematical representation of a physical system that consists of output, input, and state variables connected by a differential equation.

**Q2. Obtain the state space representation of the system y + 65 + 11y + 6y = 6u ** **where, y → output , u → input**

**Ans. **

**Q3. What is transfer function ? Also derive the expression for transfer function of a state model.**

**Ans. A. Transfer function:** Under the premise that all initial conditions are zero, it is defined as the ratio of the system’s Laplace transform’s output to input.

**B. Derivation: **

Let us consider a vector matrix differential equation

2. Now, taking Laplace transform with zero initial conditions

3. For a single-input-single-output system, Y and U are scalars.

4. Now transfer matrix can be given as

**Q4. Explain state transition matrix, its physical significance and properties. **

**Ans. A. State transition matrix:** The matrix ф(t) = exp (At) is an n xn matrix and it helps in transition from initial state X(0) to any other staterit) for t > 0, hence ф() is called state transition matrix.

**Derivation: **

1. Consider homogeneous equation, with u(t) = 0

**Q5. Find the state transition matrix for a system matrix **

**Ans. **

**Q6. Define controllability and observability in state variable analysis **

**Ans. A. Controllability:**

1. If the desired state of the system can be changed over a specific time period by applying input, the system is said to be controllable.

2. Consider n^{th} order multiple input linear time invariant system represented by its state equation as, ** **

3. The necessary and sufficient condition for the system to be completely state controllable is that the rank of the composite matrix Q_{c} is n.

4. The composite matrix Q_{c} is given by,

**B. Observability:**

1. If all of a system’s state can be ascertained using information about the output of the system at a particular time, the system is said to be observable.

2. State equation

3. The system is completely observable if and only if the rank of the composite matrix Q_{o} is n.

4. Composite matrix Q_{o} is given by,

Important Question with solutions | AKTU Quantums | Syllabus | Short Questions

## Basic Signal And System Quantum, Syllabus, Important Questions

Label | Link |
---|---|

Subject Syllabus | Syllabus |

Short Questions | Short-question |

Important Unit-1 | Unit-1 |

Important Unit-2 | Unit-2 |

Important Unit-3 | Unit-3 |

Important Unit-4 | Unit-4 |

Important Unit-5 | Unit-5 |

Question paper – 2021-22 | 2021-22 |

## Basic Signal And System Quantum PDF: | AKTU Quantum PDF:

Quantum Series | Links |

Quantum -2022-23 | 2022-23 |

## AKTU Important Links | Btech Syllabus

Link Name | Links |
---|---|

Btech AKTU Circulars | Links |

Btech AKTU Syllabus | Links |

Btech AKTU Student Dashboard | Student Dashboard |

AKTU RESULT (One VIew) | Student Result |

## 2 thoughts on “UNIT 04 STATE VARIABLE ANALYSIS | Basic Signal and Systems -AKTU”