Interval observer design for estimation and control of time-delay descriptor systems

Efimov, Denis; Polyakov, Andrey; Richard, Jean‐Pierre

doi:10.1016/j.ejcon.2015.01.004

Cited by 70 publications

(51 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and can be used for design purposes (e.g. for the design of interval observers [8][9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

Stability and performance analysis of linear positive systems with delays using input–output methods

Briat

2017

International Journal of Control

View full text Add to dashboard Cite

It is known that input-output approaches based on scaled small-gain theorems with constant Dscalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with uncertain linear operators. This dramatically contrasts with the case of general linear systems with delays where input-output approaches provide, in general, sufficient conditions only. Using these results we provide simple alternative proofs for many of the existing results on the stability of linear positive systems with discrete/distributed/neutral time-invariant/-varying delays and linear difference equations. In particular, we give a simple proof for the characterization of diagonal Riccati stability for systems with discrete-delays and generalize this equation to other types of delay systems. The fact that all those results can be reproved in a very simple way demonstrates the importance and the efficiency of the input-output framework for the analysis of linear positive systems. The approach is also used to derive performance results evaluated in terms of the L1-, L2-and L∞-gains. It is also flexible enough to be used for design purposes.

show abstract

“…and can be used for design purposes (e.g. for the design of interval observers [8][9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

Stability and performance analysis of linear positive systems with delays using input–output methods

Briat

2017

International Journal of Control

View full text Add to dashboard Cite

show abstract

“…By induction, if e(0) ≥ 0 and e(0) ≥ 0, then the relations e(t) ≥ 0, e(t) ≥ 0 are preserved for all t ≥ 0 [32]. Therefore, from (13) the inclusion (14) is valid.…”

Section: Remark 11mentioning

confidence: 98%

“…. , l. Then the interval observer (13), (20) for the system (7) admits the relations (14). If in addition there exist symmetric matrices P ∈ R 2n×2n , Σ ∈ R 2n×2n , Ξ ∈ R 2n×2n and Θ ∈ R 2n×2n such that the LMIs (15) are satisfied for…”

Section: Remark 11mentioning

confidence: 99%

“…A peculiarity of an interval observer is that in addition to stability conditions, some restrictions on positivity of estimation error dynamics have to be imposed (in order to envelop the system solutions). The existing solutions in the field [23,12,14,26] are based on the delay-independent conditions of positivity from [18,2]. Some results on interval observer design for uncertain time-varying delay can be found in [28,12].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Linear interval observers under delayed measurements and delay-dependent positivity

Efimov¹,

Fridman²,

Polyakov³

et al. 2016

Automatica

Self Cite

View full text Add to dashboard Cite

New interval observers are designed for linear systems with time-varying delays in the case of delayed measurements. Interval observers employ positivity and stability analysis of the estimation error system, which in the case of delayed measurements should be delay-dependent. New delay-dependent conditions of positivity for linear systems with time-varying delays are introduced. Efficiency of the obtained solution is demonstrated on examples.

show abstract

“…An advantage of interval observer is that it allows many types of uncertainties to be taken into account in the system. The interval observer design techniques have been developed for many types of models: continuous-time [38], [48], [9], discrete-time [16], [39], [21], [40], time-delay [41], [17], [18] and algebraic-differential [19] ones.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of linear impulsive systems under dwell-time constraints: Interval observer-based framework

Degue

Efimov

Richard

2018

European Journal of Control

Self Cite

View full text Add to dashboard Cite

The problem of interval observer design is studied for a class of linear impulsive systems. Ranged and minimum dwell-time constraints are considered under detectability assumption. The first contribution of this paper lies in designing interval observers for linear impulsive systems under ranged and minimum dwelltime constraints, and investigating positivity of the estimation error dynamics in addition to stability. Several observers are designed oriented on different conditions of positivity and stability for estimation error dynamics. The boundedness of the estimation error (input-to-state stability property) and the observer stability conditions are stated as infinite-dimensional linear programming problems. Next, an output stabilizing feedback design problem is discussed, where the stability is checked using linear matrix inequalities (LMIs). Efficiency of the proposed approach is demonstrated by computer simulations for a commercial electric vehicle equipped with a low power range extender fuel cell, a bouncing ball, an academic linear impulsive system and for Fault Detection and Isolation (FDI) and Fault-Tolerant Control (FTC) of a power split device with clutch for heavy-duty military vehicles.

show abstract

Interval observer design for estimation and control of time-delay descriptor systems

Cited by 70 publications

References 32 publications

Stability and performance analysis of linear positive systems with delays using input–output methods

Stability and performance analysis of linear positive systems with delays using input–output methods

Linear interval observers under delayed measurements and delay-dependent positivity

Stabilization of linear impulsive systems under dwell-time constraints: Interval observer-based framework

Contact Info

Product

Resources

About