Signals and Systems

9.2 CONCEPTS OF STATE, STATE VARIABLES AND STATE MODEL

• State: The state of a dynamic system is the smallest set of variables and the knowledge of these variables at t = t₀ together with inputs for t ≥ t₀ completely determines the behaviour of the system at t ≥ t₀. A compact and concise representation of the past history of the system can be termed as the state of the system.
• State Variables: The smallest set of variables that determine the state of the system are known as state variables.

  The knowledge of capacitor voltage at t = 0 i.e., the initial voltage of the capacitor is a history dependent term and it forms a state variable. Similarly, initial current in an inductor is treated as state variable.

• State Vector: The ‘n’ state variables that ...