18th IFAC World Congress, Milano, Italy; 08/2011
ABSTRACT: Prior results on input reconstruction for multi-input, multi-output discrete-time linear systems are extended by defining
l-delay input and initial-state observability. This property provides the foundation for reconstructing both unknown inputs
and unknown initial conditions, and thus is a stronger notion than l-delay left invertibility, which allows input reconstruction only when the initial state is known. These properties are linked
by the main result (Theorem4), which states that a MIMO discrete-time linear system with at least as many outputs as inputs
is l-delay input and initial-state observable if and only if it is l-delay left invertible and has no invariant zeros. In addition, we prove that the minimal delay for input and state reconstruction
is identical to the minimal delay for left invertibility. When transmission zeros are present, we numerically demonstrate
l-delay input and state reconstruction to show how the input-reconstruction error depends on the locations of the zeros. Specifically,
minimum-phase zeros give rise to decaying input reconstruction error, nonminimum-phase zeros give rise to growing reconstruction
error, and zeros on the unit circle give rise to persistent reconstruction error.
KeywordsUnknown inputs-Left invertibility-Invariant zeros-Markov parameters-Toeplitz matrix
Circuits Systems and Signal Processing 02/2011; 30(1):233-262. · 0.82 Impact Factor
ABSTRACT: Unknown-state, unknown-input reconstruction in systems with invariant zeros is intrinsically limited by the fact that, for any invariant zero, at least one initial state exists, s.t. when the mode of the invariant zero is suitably injected into the system, the output remains identically equal to zero. Nonetheless, the problem has recently attracted considerable interest, mainly due to its connections with fault diagnosis and fault tolerant issues. This paper discusses the synthesis of a system capable of reconstructing the generic initial state and the generic bounded input in discrete-time nonminimum-phase linear systems with feedthrough terms. The procedure described is developed within the geometric approach.
Decision and Control (CDC), 2010 49th IEEE Conference on; 01/2011
ABSTRACT: As an extension of existing results on input reconstruction, we define l-delay state and input reconstruction, and we characterize this property through necessary and sufficient conditions. This property is shown to be a stronger notion of left invertibility, in which the initial state is assumed to be known. We demonstrate l-delay state and input reconstruction on several numerical examples, which show how the input reconstruction error depends on the locations of the zeros. Specifically, minimum-phase zeros give rise to decaying input reconstruction error, nonminimum-phase zeros give rise to growing reconstruction error, and zeros on the unit circle give rise to persistent reconstruction error.
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 01/2010
2009 AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois, USA; 08/2009