Linear Systems

basicaLinear System Structures

The basic structural properties of the state-space representation in a linear dynamical system, such as: controllability, observability, invariant zeros, structure at infinity, etc., are analyzed. These structural properties are fundamental in the analysis and solution of some control problems. The problem of structural modification of multivariable systems under irregular state feedback is also considered.

basicaMultivariable System Decoupling

The problem of multivariable linear system decoupling consists basically of finding a control action, typically state feedback control, such that in the feedback system each of the new entries controls one and only one of the system outputs. This will achieve maintaining the schematic relatively simple, where the influence of each input is reflected in an output of the system without affecting anything else. This structure is desirable in practical applications of multivariable systems.

Robustness is a highly desirable property in a control or supervision system, i.e., the system should be able to preserve a property despite the presence of noise or uncertainty in said system. The two most sought after properties when designing a supervision or control system are: Robustness and stability, and/or robust performance. In linear systems, the technique for designing robust control is the H-infinity method.