Observability of Linear Hybrid Systems

Vidal, René; Chiuso, Alessandro; Soatto, Stefano; Sastry, S. Shankar

doi:10.1007/3-540-36580-x_38

Cited by 186 publications

(144 citation statements)

References 14 publications

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“…The two conditions (17) and (18), which must be simultaneously satisfied, are obviously in contradiction with (13) or (14). This completes the proof of sufficiency.…”

Section: Observability Before the First Switchsupporting

confidence: 58%

“…[4] derives conditions for the observability of autonomous discrete-time JLSs that can be tested using simple rank tests on the structural parameters of the model. Such conditions are natural generalizations of well-known results for linear systems and can be extended to continuous-time JLSs [14] and to piecewise affine hybrid systems [15]. [16] gives observability conditions for stochastic linear hybrid systems in terms of the covariances of the outputs.…”

Section: Introductionmentioning

confidence: 90%

“…So, we only need to show that condition (14) in Lemma 1 holds if and only if at least one of the Markov parameters of each linear system is different from the Markov parameters of other linear systems. This is equivalent to proving that condition (18) holds if and only if the Markov parameters of any two linear systems are equal to each other.…”

Section: Observability Before the First Switchmentioning

confidence: 99%

See 2 more Smart Citations

Rank tests for the observability of discrete-time jump linear systems with inputs

Elhamifar

Petreczky

Vidal

2009

2009 American Control Conference

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Abstract-We analyze the observability of the continuous and discrete states of discrete-time jump linear systems (JLSs) with deterministic inputs. We consider several definitions of observability for JLSs depending on whether some or all inputs are considered. Unfortunately, checking these definitions can involve an exponential number of rank tests on the parameters of the JLS when the discrete state sequence is arbitrary. Our key contribution is to demonstrate that when there is a minimum separation between consecutive switches, one can verify observability by checking a number of rank tests that is only quadratic in the number of discrete states. The observability conditions we derive are natural generalizations of the well known rank test for linear systems. Moreover, they can be related to the Markov parameters of the individual linear systems.

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“…The two conditions (17) and (18), which must be simultaneously satisfied, are obviously in contradiction with (13) or (14). This completes the proof of sufficiency.…”

Section: Observability Before the First Switchsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 90%

Section: Observability Before the First Switchmentioning

confidence: 99%

See 1 more Smart Citation

Rank tests for the observability of discrete-time jump linear systems with inputs

Elhamifar

Petreczky

Vidal

2009

2009 American Control Conference

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“…Work on identification/filtering of hybrid systems first appeared in the seventies (see [19] for a review). More recent works consider variations of Problem 1 in which the model parameters, the discrete state and/or the switching mechanism are known, and concentrate on the analysis of the observability of the hybrid state [2], [4], [9], [11], [18], [21], [22] and the design of hybrid observers [1], [3], [7], [8], [10], [12], [14], [16], [17], [20].…”

Section: Problemmentioning

confidence: 99%

Identification of PWARX hybrid models with unknown and possibly different orders

Vidal

2004

Proceedings of the 2004 American Control Conference

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Abstract-We consider the problem of identifying the orders and the model parameters of PWARX hybrid models from noiseless input/output data. We cast the identification problem in an algebraic geometric framework in which the number of discrete states corresponds to the degree of a multivariate polynomial p and the orders and the model parameters are encoded on the factors of p. We derive a rank constraint on the input/output data from which one can estimate the coefficients of p. Given p, we show that one can estimate the orders and the parameters of each ARX model from the derivatives of p at a collection of regressors that minimize a certain objective function. Our solution does not require previous knowledge about the orders of the ARX models (only an upper bound is needed), nor does it constraint the orders to be equal. Also the switching mechanism can be arbitrary, hence the switches need not be separated by a minimum dwell time. We illustrate our approach with an algebraic example of a switching circuit and with simulation results in the presence of noisy data.

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“…A generic setting for the observability of switched linear systems in a continuous setting has been given in Babaali and Pappas [2005]. In Vidal et al [2003] the observability of switched linear systems in the case of deterministic switching signal was carried out. The unobserved switching case was analyzed in De Santis et al [2003].…”

Section: Introductionmentioning

confidence: 99%

Real-time estimation of the switching signal for perturbed switched linear systems

Fliess

Join

Perruquetti³

2009

IFAC Proceedings Volumes

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We extend previous works of on the estimation of the switching signal and of the state for switching linear systems to the perturbed case when the perturbation is structured that is when the perturbation is unknown but known to satisfy a certain differential equation (for example if the perturbation is constant then its time-derivative is zero). We characterize also singular inputs and/or perturbations for which the switched systems become undistinguishable. Several convincing numerical experiments are illustrating our techniques which are easily implementable.

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Observability of Linear Hybrid Systems

Cited by 186 publications

References 14 publications

Rank tests for the observability of discrete-time jump linear systems with inputs

Rank tests for the observability of discrete-time jump linear systems with inputs

Identification of PWARX hybrid models with unknown and possibly different orders

Real-time estimation of the switching signal for perturbed switched linear systems

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