Observer design for a class of piece-wise affine systems

Observer Designs for Experimental Non-Smooth and Discontinuous Systems

“…In [10] and [11], it is proven that the state estimation error of a model-based observer for a Lipschitzian system with slope-restricted possibly monotone multivariable nonlinearities, exponentially converges to zero. In [12], switched observers are considered for a class of bimodal PWL systems. The observer design strategy employed there provides sufficient conditions, under which global asymptotic stability of the state estimation error can be achieved if the system dynamics is continuous over the switching plane.…”

“…The design in [13] is based on ideas in [14], in which monotone multivalued mappings were first introduced in the control community. It is a distinguishing feature of the observer structures in [10], [12], and [13] that the observers do not need knowledge about the active mode of the system, in contrast to those in [8] and [9]. A difference between [10] and [12], for the bimodal case, is that the observer design in [10] implies that the same observer gain is used for both modes, while in [12], different observer gains are used for every mode.…”

“…A difference between [10] and [12], for the bimodal case, is that the observer design in [10] implies that the same observer gain is used for both modes, while in [12], different observer gains are used for every mode. A difference between [10], [12], and [13] is that the results of [10] are applicable to locally Lipschitzian systems while the results of [12] and [13] can also be applied to non-smooth, non-Lipschitzian systems.…”

Observability of Switched Linear Systems in Continuous Time

“…However, most of the resulting literature is not related to the problems under consideration here. For instance, while the work in [6,11,12,15,23] was carried out in a stochastic setting, the papers [3,5,9,18,13] studied observability of hybrid linear systems, where the modes depend on the state trajectory, and deterministic discrete-time switched linear systems were considered in [1,21]. However, in contrast to classical linear systems, there are differences between the discrete and continuous time cases in switched linear systems, which require them to be studied independently.…”

Convergent piecewise affine systems: analysis and design Part I: continuous case

“…This convergence property of a system plays an important role in many (nonlinear) control problems including tracking, synchronization, observer design, the output regulation problem and performance analysis of nonlinear systems see e.g. [1], [2], [3], [4], [5] and references therein.…”