Eigenstructure Assignment for Componentwise Ultimate Bound Minimization in Discrete-Time Linear Systems

• Published in: IEEE transactions on automatic control Vol. 61; no. 11; pp. 3669 - 3675
• Main Authors: Heidari, Rahmat, Seron, Maria M., Braslavsky, Julio H.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Design engineering; Discrete time systems; Disturbances; Eigenvalues and eigenfunctions; Electric potential; Linear matrix inequalities; Linear systems; Linear time-invariant (LTI); Minimization; Optimization; State feedback; Trajectory; ultimate-bounds (UBs); Voltage
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2513367

This technical note presents a feedback design approach to minimise state ultimate-bounds (UBs) in linear time-invariant discrete-time systems subject to non-vanishing bounded disturbances. A target closed-loop eigenstructure is first constructed to achieve the lowest possible UBs for one or more state components of the system. Structural conditions on the system matrices are then derived to guarantee that the target eigenstructure can be assigned by state feedback. When the required structural conditions are satisfied, an eigenvector assignment procedure can be applied to simultaneously minimise multiple UBs in systems with multiple inputs. The results are illustrated by a numerical example drawn from a distributed voltage control problem in inverter-based microgrids.