## State Space ModelThe process by which the state of a system is determined is called state variable analysis. ## Advantages of State Space Techniques- This technique can be used for linear or nonlinear, time-variant or time-invariant systems.
- It is easier to apply where Laplace transform cannot be applied.
- The nth order differential equation can be expressed as 'n' equation of first order.
- It is a time domain method.
- As this is time domain method, therefore this method is suitable for digital computer computation.
- On the basis of the given performance index, this system can be designed for an optimal condition.
## State Space representation of electrical system:Consider an RLC network, At time t = 0 Current = i Thus, the state of the network at time t=0 is specified by the inductor current and capacitor voltage. Therefore i Apply KVL Also, From eq.1 This type of equation is called State equation. And the variables present in this equation are called state variables. Eq. 3 and Eq. 4 can be written in matrix form as The general form of state equation is Y = n- dimensional output vector U = r-dimensional control vector or input vector A = n × n system matrix B = n × r control matrix C = n × n output matrix When there is no direct connection between input and output in that case D u(t) is not taken.
For the nth order differential equation ## Example 1A system is described by the differential equation Where y is the output and u is the input to the system. Obtain the state space representation of the system. ## Solution |

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