Observability of the discrete state for dynamical piecewise hybrid systems

Chaib, Salim; Boutat, Driss; Benali, Abderraouf; Barbot, Jean Pierre

doi:10.1016/j.na.2005.05.028

Cited by 42 publications

(17 citation statements)

References 10 publications

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“…if n ), j = 1, 2 in order to know the operating region where the system evolves (see [7] or [11] for more details on the geometrical conditions establishing this region). 13 2.…”

Section: Switched Systemmentioning

confidence: 99%

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Floquet

Barbot

2007

International Journal of Systems Science

180

107

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. Super twisting algorithm based step-by-step sliding mode observers for nonlinear systems with unknown inputs. International Journal of Systems Science, Taylor Francis, 2007, 38 (10), pp.803-815. inria-00128137v2 Super twisting algorithm based step-by-step sliding mode observers for nonlinear systems with unknown inputsThis paper highlights the interest of step-by-step higher order sliding mode observers for MIMO nonlinear systems with unknown inputs. A structural matching condition, stating on the possibility to design such observers and to reconstruct the unknown inputs, is derived. A finite time sliding mode observer, based on the hierarchical use of the super twisting algorithm, is developed. Then, it is shown that this observer is of interest in the field of hybrid systems and systems with observability singularities. Lastly, it is shown through an example how to relax the usual matching condition by the means of this type of finite time sliding mode observer.

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“…if n ), j = 1, 2 in order to know the operating region where the system evolves (see [7] or [11] for more details on the geometrical conditions establishing this region). 13 2.…”

Section: Switched Systemmentioning

confidence: 99%

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Floquet

Barbot

2007

International Journal of Systems Science

180

107

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“…The study of this class of systems dates back to the early works of Andronov on oscillation in nonlinear systems, Kalman on saturated linear systems in 1950s. This field has received much attention over the past two decades [1][2][3][4][5][6][7][8][9][10][11][12]. However, most of these works are based on the assumption that this class of systems is well-posed.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solutions of piecewise nonlinear systems

Teo

Rehbock

et al. 2009

Nonlinear Analysis: Theory, Methods & Applications

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“…This alone constitutes a challenging task and has attracted a considerable amount of research on observability of hybrid and switched systems (e.g. [8]- [10]) and put forth various switching signal estimators and observers for hybrid and switched systems.…”

Section: A Hybrid Switching State Observersmentioning

confidence: 99%

An alternative approach to switching hyperplane estimation in PWA systems

Kersting

Buss

2015

2015 American Control Conference (ACC)

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Abstract-Usually the identification of piecewise affine systems consists of two steps. First, subsystem parameters are identified before the state space partition is reconstructed. For the later step, it is common to label the states of a recorded trajectory and separate differently labeled states with the help of linear support vector machines. In this paper, we present an alternative approach to estimate switching hyperplanes in continuous time piecewise affine systems. The presented approach builds upon three components. First, a hybrid observer reconstructs the switching signal up to a bounded delay. Second, we remove the delay in the reconstructed switching signal by solving an optimization problem. We obtain more precise switching states that lie on a specific switching hyperplane. Third, the switching hyperplanes are fitted to the switching states with Total Least Squares. The paper illustrates the presented approach on a numerical example.

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Observability of the discrete state for dynamical piecewise hybrid systems

Cited by 42 publications

References 10 publications

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Existence and uniqueness of solutions of piecewise nonlinear systems

An alternative approach to switching hyperplane estimation in PWA systems

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