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Finite settling time stabilization for linear multivariable time-invariant discrete-time systems: An algebraic approach

Milonidis, E. (1994). Finite settling time stabilization for linear multivariable time-invariant discrete-time systems: An algebraic approach. (Unpublished Doctoral thesis, City, University of London)

Abstract

The problem of Total Finite Settling Time Stabilization of linear time-invariant discrete-time systems is investigated in this thesis. This problem falls within the same area of the well-known deadbeat (time-optimal) control and in particular, constitutes a generalization of this problem. That is, instead of seeking time-optimum performance, it is required that all internal and external variables (signals) of the closed-loop system settle to a new steady state after a finite time from the application of a step change to any of its inputs and for every initial condition. The state/output deadbeat control is a special case of the Total FSTS problem.

Using a mathematical and system theory framework based on sequences and the polynomial equation (algebraic) approach, we are able to tackle the FSTS problem in a unifying manner. The one-parameter (unity) feedback configuration is mainly used for the solution of the FSTS problem and FSTS related control strategies. The whole problem is reduced to the solution of a polynomial matrix Diophantine equation which guarantees not only internal stability but also internal FSTS and is further reduced to the solution of a linear algebra problem over R. This approach enables the parametrizat ion of the family of all FSTS controllers, as well as those which are causal, in a Youla-Bongiorno-Kucera type parametrization.

The minimal McMillan degree FSTS problem is completely solved for vector plants and a parametrization of the FSTS controllers according to their McMillan degree is obtained. In the MIMO case bounds of the minimum McMillan degree controllers are derived and families of FSTS controllers with given lower/upper McMillan degree bounds are provided in parametric form.

Having parametrized the family of all FSTS controllers, the state deadbeat regulation is treated as a special case of FSTS and complete parametrization of all the deadbeat regulators is presented. In addition, further performance criteria, or design constraints are imposed such as, FSTS tracking and/or disturbance rejection, partial assignment of controller dynamics, l1-, l∞-optimization and robustness to plant parameter variations.

Finally, the Simultaneous-FSTS problem is formulated, and necessary as well as sufficient conditions for its solution are derived. Also, a two-parameter control scheme is introduced to alleviate some of the drawbacks of the one-parameter control. A parametrization of the family of FSTS controllers as well as the FSTS controllers for tracking and/or disturbance rejection is given as an illustration of the particular advantages of the two-parameter FSTS controllers.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
Departments: School of Science & Technology > Engineering > Electrical & Electronic Engineering
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
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