Is the inverse system of causal system causal?

The inverse system of causal system is causal. Inverse system refers to a system that has some opposite input-output transfer relationship with a given system.

Among the related concepts of inverse system, left inverse system and right inverse system are two basic classification methods. Inverse system theory is widely used in many aspects of control theory, such as disaster solving, model matching, minimum design, definition and solution of zero point of multivariable linear system, inverse system method of multivariable nonlinear system design, coding theory, filtering, game theory and so on.

A dynamic system described by a nonlinear differential equation or difference equation. A nonlinear system is called a nonlinear control system unless it contains control terms. The nonlinearity of the control system may come from the controlled system itself, or it may be caused by nonlinear components in the controller design. There are two kinds of nonlinear systems discussed most in control theory: general nonlinear systems and affine nonlinear systems.

relevant information

General systems are nonlinear, while linearity is only an approximation and a special case. The geometric theory of nonlinear systems developed since 1970s is to study nonlinear systems by differential geometry method, which has achieved great success in system structure analysis and related control design, such as feedback linearization and decoupling.

In the stability analysis and stabilization design of nonlinear systems, many new control methods have also emerged, such as energy-based control method, backstepping method and sliding mode control. Because almost all practical systems are nonlinear, the dynamic analysis and control design of nonlinear systems have become the main research objectives of control theory.