Observability of Switched Linear Systems in Continuous Time

Babaali, M.; Pappas, George J.

doi:10.1007/978-3-540-31954-2_7

Cited by 108 publications

(102 citation statements)

References 22 publications

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“…. , N }, is assumed, as in (Babaali and Pappas, 2005), to be right-continuous and only a finite number of jumps can occur in any finite interval. The discrete mode observability is the capacity to deduce the discrete mode knowing the measurements.…”

Section: { E R(t)ẋ (T) = a R(t) X(t) Y(t) = C R(t) X(t)mentioning

confidence: 99%

Discrete mode observability of structured switching descriptor linear systems: A graph-theoretic approach

Boukhobza¹,

Hamelin²

2013

Automatica

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To cite this version:Taha Boukhobza, Frédéric Hamelin. Discrete mode observability of structured switching descriptor linear systems: A graph-theoretic approach. Automatica, Elsevier, 2013, 49 (10) AbstractThe main result of the paper consists in graphical necessary and sufficient conditions which ensure the generic discrete mode observability of structured switching descriptor systems. The methods used in the previous studies on the observability of switching linear systems on standard form are not applicable to switching descriptor systems. So, we develop a new approach starting from bipartite representations of these systems and then building a new kind of digraph dedicated to the discrete mode observability study. The proposed method assumes only the knowledge of the system's structure and is applicable to a large class of descriptor systems including regular and non regular systems even if they are square or under-determined. The provided conditions can be implemented by classical graph-theory algorithms.

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Section: { E R(t)ẋ (T) = a R(t) X(t) Y(t) = C R(t) X(t)mentioning

confidence: 99%

Discrete mode observability of structured switching descriptor linear systems: A graph-theoretic approach

Boukhobza¹,

Hamelin²

2013

Automatica

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“…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. First assume that the first 2n Markov parameters of two different linear models corresponding to q t0 andq t0 are equal to each other.…”

Section: Observability Before the First Switchmentioning

confidence: 99%

“…First assume that the first 2n Markov parameters of two different linear models corresponding to q t0 andq t0 are equal to each other. By using the Cayley-Hamilton Theorem [5], one can easily show that Γ T (q t0 )−Γ T (q t0 ) = 0 and we immediately get the condition in equation (18). Next, assume that equation (18) holds but at least one of the Markov parameters of the linear system q t0 andq t0 are different from each other.…”

Section: Observability Before the First Switchmentioning

confidence: 99%

“…[1] proposes various concepts of observability for autonomous and non-autonomous JLSs without imposing constraints on time separation between switches. [18] studies the observability of autonomous and non-autonomous continuous-time switched linear systems and shows that the observability of the discrete mode is equivalent to controlled-discernibility of pairs of different modes.…”

Section: Introductionmentioning

confidence: 99%

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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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“…In Ackerson and Fu [1970], the notion of state estimation for switched systems is introduced. 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.…”

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 Switched Linear Systems in Continuous Time

Abstract: Abstract. We study continuous-time switched linear systems with unobserved and exogenous mode signals. We analyze the observability of the initial state and initial mode under arbitrary switching, and characterize both properties in both the autonomous and non-autonomous cases.

Cited by 108 publications

References 22 publications

Discrete mode observability of structured switching descriptor linear systems: A graph-theoretic approach

Discrete mode observability of structured switching descriptor linear systems: A graph-theoretic approach

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

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

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