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This article introduces the notion of absolutely distinguishable discrete‐time dynamic systems, with particular applicability to linear time‐invariant and linear parameter‐varying systems. The motivation for this novel type of distinguishability stems, in particular, from the stability and performance requirements of worst‐case adaptive control methodologies. The main results presented herein show that, in most practical cases, a persistence of excitation type of condition and a minimum number of iterations are required to properly distinguish two dynamic systems. We also demonstrate that the former constraint can be written as a lower bound on the intensity of the exogenous disturbances. The applicability of the developed theory is illustrated with a set of examples. [ABSTRACT FROM AUTHOR]

In the context of fault detection and isolation of linear parameter-varying systems, a challenging task appears when the dynamics and the available measurements render the model unobservable, which invalidates the use of standard set-valued observers. Two results are obtained in this paper, namely, using a left-coprime factorization, one can achieve set-valued estimates with ultimately bounded hyper-volume and convergence dependent on the slowest unobservable mode; and by rewriting the set-valued observer equations and taking advantage of a coprime factorization, it is possible to have a low-complexity fault detection and isolation method. Performance is assessed through simulation, illustrating, in particular, the detection time for various types of faults. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This article introduces a new method for model falsification using set-valued observers, which can be applied to a class of discrete linear time-invariant dynamic systems with time-varying model uncertainties. In comparison with previous results, the main advantages of this approach are as follows: The computation of the convex hull of the set-valued estimates of the state can be avoided under certain circumstances; to guarantee convergence of the set-valued estimates of the state, the required number of previous steps is at most as large as the number of states of the nominal plant; and it provides a straightforward nonconservative method to falsify uncertain models of dynamic systems, including open-loop unstable plants. The results obtained are illustrated in simulation, emphasizing the advantages and shortcomings of the suggested method. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY A multiple-model adaptive control methodology is proposed that is able to provide stability and performance guarantees, for uncertain linear parameter-varying plants. The identification problem is addressed by taking advantage of recent advances in model falsification using set-valued observers (SVOs). These SVOs provide set-valued estimates of the state of the system, according to its dynamic model. If such estimate is the empty set, the underlying dynamic model is invalidated, and a different controller is connected to the loop. The behavior of the proposed control algorithm is demonstrated in simulation, by resorting to a mass-spring-dashpot system. As a caveat, the computational burden associated with the SVOs can be prohibitive under some circumstances. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]