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Matrix C. Matrix C is the output matrix, and determines the relationship between the system state and the system output. Matrix D. Matrix D is the feed-forward matrix, and allows for the system input to affect the system output directly.

The state equation has a single first order derivative of the state vector on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side. The output equation has the output on the left, and the state vector, q(t), and the input u(t) on the right.

State Space Model from Differential Equation So, the number of the state variables is equal to two and these state variables are the current flowing through the inductor, i(t) and the voltage across capacitor, vc(t). From the circuit, the output voltage, v0(t) is equal to the voltage across capacitor, vc(t).

The control law is a mathematical expression which describes the function implemented by an augmentation or autopilot controller. For example, a very simple and very commonly used control law describing an inner-loop control system for augmenting yaw damping is.

State-space notation is a set of matrix equations which describe how a system will evolve over time. These equations relate the change in state , and the output , to linear combinations of the current state vector and input vector . State-space control can deal with continuous-time and discrete-time systems.

In control engineering, model based fault detection and system identification a state-space representation is a mathematical model of a physical system specified as a set of input, output and variables related by first-order (not involving second derivatives) differential equations or difference equations.

The basic technique to isolate a variable is to ?do something to both sides? of the equation, such as add, subtract, multiply, or divide both sides of the equation by the same number. By repeating this process, we can get the variable isolated on one side of the equation.