Output regulation for switched linear systems with different coordinate transformations

Abstract

Dimirovski, Georgi M. (Dogus Author) -- Conference full title: The 2012 UKACC International Conference on Control : Cardiff, UK, 3-5 September 2012 : proceedingsThis paper addresses the output regulation problem for switched linear systems. When each regulation equation has their own solution, we give a sufficient condition for the output regulation problem to be solvable. Firstly, we give the regulation equations of switched linear systems and the relation of the transformed states between two consecutive switching times. Secondly, the existence of a minimal average dwell-time for every switching sequence is assumed, and by virtue of an appropriate Lyapunov analysis, the output regulation is achieved. Our result is of much less conservativeness.University of Glamorga

Almost output regulation of discrete-time switched linear systems

“…Necessary and sufficient conditions for the output regulability of switched linear systems with arbitrary switching were derived in [15] using the CLF approach. This result was further extended by [16], [13] using the ADT technique with MLFs. One common limitation of these results is that the external signals (including the reference inputs and/or the disturbances) are assumed to be generated by a single neutrally stable exosystem.…”

“…Consequently, condition (16) can be deduced. The controller formula (17) can be verified by inverting the relations in (24) and (27).…”

Almost output regulation of switched linear dynamics with switched exosignals

“…As mentioned in the introduction, one of the technical difficulties that arises in the synthesis is that different coordinate transformations are needed for different subsystems. This difficulty has been overcome in the earlier proof by introducing a new coordinate transformation as in (23). Unlike those typically used in the literature [2,8,23], it results in a particular switched system with independent dynamics in each subsystem as seen in (24).…”

“…This difficulty has been overcome in the earlier proof by introducing a new coordinate transformation as in (23). Unlike those typically used in the literature [2,8,23], it results in a particular switched system with independent dynamics in each subsystem as seen in (24). Based on this transformation technique and the new hybrid controller structure (14) with impulsive dynamics, the convex synthesis conditions as described in Theorem 1 are derived.…”

“…For LTI systems, the output regulation problem would usually boil down to asymptotic stabilization of a transformed system after decoupling the references/disturbances from the original system states through a coordinate transformation. However, since each subsystem of switched linear systems has different dynamics, it is difficult to find a common state transformation that is suitable for all subsystems . Thus, the questions of how to establish stability analysis and efficient synthesis conditions for switched linear systems have to be answered first.…”