If the new g(s) is controlled, then the realization is not completely observable; It is not completely controllable to realize considerable realization. At this time, the solved system will be larger than the original system by 1, but the transfer function is the same, so don't worry, we just add the omitted items.
State space representation is a mathematical model that represents a physical system as a set of inputs, outputs and states. The relationship among inputs, outputs and states can be described by many first-order differential equations.
In order to make the mathematical model independent of the number of inputs, outputs and states, the inputs, outputs and states are expressed in the form of vectors, while the differential equations (which can be transformed into algebraic equations if they are linear time-invariant systems) are expressed in the form of matrices.
Extended data:
The application scope of the concept of transfer function is limited to linear ordinary differential equations. Of course, the transfer function method is widely used in the analysis and design of such systems. The following are some important explanations about the transfer function (systems described by linear ordinary differential equations are all involved in the following descriptions):
The transfer function of the system is a mathematical model, which represents an operation method of differential equations connecting output variables and input variables.
The transfer function is a property of the system itself, which has nothing to do with the size and nature of the input or driving function.
The transfer function contains the necessary units to connect input and output, but it does not provide any information about the physical structure of the system (many physically completely different systems can have the same transfer function, which is called similar systems);
Baidu Encyclopedia-Transfer Function