Stable inversion of LPTV systems with application in position-dependent and non-equidistantly sampled systems. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: van Zundert, Jurgen; Oomen, Tom
• Is Part Of: International journal of control. Volume 92:Issue 5(2019)
• Page Start: 1022
• Page End: 1032
• Publication Date: 2019-05-04
• Subjects: Stable inversion -- dichotomy -- linear time-varying systems -- linear periodically time-varying systems -- tracking control; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2017.1380315
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: Many control applications, including feedforward and learning control, involve the inverse of a dynamical system. For nonminimum-phase systems, the response of the inverse system is unbounded. For linear time-invariant (LTI), nonminimum-phase systems, a bounded, noncausal inverse response can be obtained through an exponential dichotomy. For generic linear time-varying (LTV) systems, such a dichotomy does not exist in general. The aim of this paper is to develop an inversion approach for an important class of LTV systems, namely linear periodically time-varying (LPTV) systems, which occur in, e.g. position-dependent systems with periodic tasks and non-equidistantly sampled systems. The proposed methodology exploits the periodicity to determine a bounded inverse for general LPTV systems. Conditions for existence are provided. The method is successfully demonstrated in several application cases, including position-dependent and non-equidistantly sampled systems.