the state variable description of disecre state space system is given by [ X 1 (k+1)X 2 (k+1) ]=[ −0.2−100.8 ][ X 1 (k)X 2 (k) ]+[ 11 ]u(k);y(k)=[ −1 1 ][ X 1 (k)X 2 (k) ]

The state variable description of a discrete state space system is a mathematical model that represents the behavior of the system over time using state variables, input variables, and output variables. It consists of equations that describe how the state of the system at the next time step depends on its current state and input, as well as how the output of the system depends on the current state and input.

Explanation:

The state variable description of a discrete state space system is a mathematical model that represents the behavior of the system over time. It consists of state variables, input variables, output variables, and the equations that govern their relationships.

In the given equation, [ X(k+1) ] = [ A ][ X(k) ] + [ B ]u(k), X(k) represents the state vector at time k, A is the state matrix, B is the input matrix, and u(k) is the input vector at time k. This equation describes how the state of the system at the next time step (k+1) depends on its current state (X(k)) and the input (u(k)).

The output equation, y(k) = [ C ][ X(k) ] + [ D ]u(k), describes how the output of the system at time k (y(k)) depends on the current state (X(k)) and the input (u(k)). C is the output matrix and D is the feedforward matrix.

By analyzing the state variable description, we can gain insights into the behavior of the system and design control strategies to achieve desired performance.

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the state variable description of disecre state space system is given by [ X 1 (k+1)X 2 (k+1)​ ]=[ −0.2−100.8 ][ X 1​ (k)X 2​ (k)​ ]+[ 11​ ]u(k);y(k)=[ −1​ 1​ ][ X 1​ (k)X 2​ (k)​ ]

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the state variable description of disecre state space system is given by [ X 1 (k+1)X 2 (k+1) ]=[ −0.2−100.8 ][ X 1 (k)X 2 (k) ]+[ 11 ]u(k);y(k)=[ −1 1 ][ X 1 (k)X 2 (k) ]