Diagonal stability of interval matrices and applications

Păstrăvanu, Octavian; Matcovschi, Mihaela-Hanako

doi:10.1016/j.laa.2010.06.016

Cited by 18 publications

(12 citation statements)

References 19 publications

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“…Such applications include solutions to optimal control problems [15], stability analysis [16,17], robotics [18], fuzzy logic [19,20], difference inequalities [21] or differential equations [22], as far as positive integers are concerned.…”

Section: Discussionmentioning

confidence: 99%

A refinement of Sándor-Tóth's inequality

2012

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Section: Discussionmentioning

confidence: 99%

A refinement of Sándor-Tóth's inequality

2012

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“…where k,i, j denotes the (i, j) entry of the matrix Δ k . In the sum appearing in (14), only the term̃i , of rank j is explained in view of the expressions (10) and (11) of i, j .…”

Section: Validation Of the Envelope Of The State Trajectorymentioning

confidence: 99%

“…Finally, according to (14), (15), and (16),x k+1,i is a sum of non-negative terms, and thus, x k+1,i ≥ x k+1,i , ie, x k+1 ≥ x k+1 . Thus, the property  k+1 has been demonstrated, and the induction principle ensures that for positive k, x k ≥ x k .…”

Section: Validation Of the Envelope Of The State Trajectorymentioning

confidence: 99%

State estimation of system with bounded uncertain parameters: Interval multimodel approach

Ichalal

Marx

Maquin

et al. 2018

Adaptive Control & Signal

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The objective of this study is the analysis of dynamic systems represented by a multimodel expression with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires the consideration of all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment.This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger-type observer, fed with the system measurements. KEYWORDSbounded uncertainties, interval observers, multimodel technique, uncertain systems INTRODUCTIONAs widely known, one of the main difficulties in system simulation, control, or estimation is dealing with uncertainties. These uncertainties may affect the input or output signals of the system (eg, unknown input, disturbance, measurement noises, etc) as well as the system model itself (eg, nonmodeled dynamics, unknown parameter, etc). The uncertainties may also be of different natures: total lack of information (unknown value of a parameter) or partial knowledge (upper and lower bounds, statistical properties, etc). This paper deals with systems with uncertain parameters.Even a low magnitude change in some parameters may have a significant impact on the system behavior and, namely, on the system state trajectory. Uncertain parameters can be considered from two main points of view: the stochastic and the deterministic ones. In the first approach, the uncertain parameters are assumed to be the results of random process realizations. It then needs to choose the probability density functions and their parameters describing the system's uncertain parameters. In the deterministic approach, no statistical models of the parameters are assumed to be available, and only the upper and lower bounds of the parameter values are known. This approach, also known as the interval approach, is adopted in this paper.The search for trajectories, which are solutions of differential inclusions, 1 were the starting point of the large amount of works on stability, stabilization, and state estimation. In the latter topic, our communication follows the pioneering work of Gouzé et al, 2 which proposed the synthesis of the interval-type observer to reconstruct the system state 480 ;32:480-493. ICHALAL ET AL. 481from measurements of inputs and outputs. Since then, many results were published on designing observers adapted to nonlinear systems with uncertain but bounded parameters. [3][4][5][6] The model-based state estimation techniques in the context of bounded uncertainties can be classified into two categories. The first one is ba...

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“…Furthermore, it can be found that the result given by Chen and Chou [20] can be viewed as a special case of (16) and (28). On the other hand, by applying the evolutionary optimization methods [38] to choose the best matrices 0 , 0 , and 0 , the conservatism of (16), (26), (28), and (29) can be reduced.…”

Section: Remark 11mentioning

confidence: 99%

“…Recently, the robustness issues of interval multiple-inputmultiple-output (MIMO) systems without state delay have been studied by many researchers (see, e.g., [16,17,[21][22][23][24][25][26][27][28][29][30][31] and references therein). But, till now, only a few researchers studied the controllability issue of the interval MIMO systems without state delay [16,[19][20][21][22][23][24][25]31].…”

Section: Introductionmentioning

confidence: 99%

Controllability Robustness of Linear Interval Systems with/without State Delay and with Unstructured Parametric Uncertainties

Chen

Chou

2013

Abstract and Applied Analysis

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The robust controllability problem for the linear interval systems with/without state delay and with unstructured parametric uncertainties is studied in this paper. The rank preservation problem is converted to the nonsingularity analysis problem of the minors of the matrix under discussion. Based on some essential properties of matrix measures, two new sufficient algebraically elegant criteria for the robust controllability of linear interval systems with/without state delay and with unstructured parametric uncertainties are established. Two numerical examples are given to illustrate the applications of the proposed sufficient algebraic criteria, where one example is also presented to show that the proposed sufficient condition for the linear interval systems having no state delay and no unstructured parametric uncertainties can obtain less conservative results than the existing ones reported recently in the literature.

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Diagonal stability of interval matrices and applications

Cited by 18 publications

References 19 publications

A refinement of Sándor-Tóth's inequality

A refinement of Sándor-Tóth's inequality

State estimation of system with bounded uncertain parameters: Interval multimodel approach

Controllability Robustness of Linear Interval Systems with/without State Delay and with Unstructured Parametric Uncertainties

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