**Q1.** Define the following:

- State
- State variables
- State vector
- State space
- State equation
- State transition matrix
- Controllaibility and
- Observability

**Ans.**

**State:**The state of a dynamic system is the smallest set of variables and the knowledge of these variables at*t*=*t*_{0}together with inputs for*t*≥*t*_{0}completely determines the behaviour of the system at*t*≥*t*_{0}.**State Variables:**The smallest set of variables that determine the state of the system are known as state variables.**State Vector:**The ‘*n*’ state variables that completely describe the behaviour of a given system are said to be ‘*n*’ components of a vector.**State Space:**The*n*dimensional space whose co-ordinate axes consist of the*x*_{1}axis,*x*_{2}axis …*x*_{n}axis ...

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