Design of Positive Linear Observers for Positive Linear Systems via Coordinate Transformations and Positive Realizations

Back, Juhoon; Astolfi, Alessandro

doi:10.1137/060663891

Cited by 83 publications

(46 citation statements)

References 18 publications

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“…The problem of Metzlerian system stabilization and observer design has been previously studied, especially for single input and single output (SISO) continuous-time linear systems, as well as discrete-time linear systems, which have minimal degree of freedom to ensure that a solution exists (see [6], [7], [8], [9] and the references therein). Applicable methods for stabilization of positive linear discrete-time systems, maintaining its positivity when using linear state feedback, are given in [10], [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Stabilization of discrete-time LTI positive systems

Krokavec

Filasová

2017

Archives of Control Sciences

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The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the statefeedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

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Section: Introductionmentioning

confidence: 99%

Stabilization of discrete-time LTI positive systems

Krokavec

Filasová

2017

Archives of Control Sciences

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“…[13][14][15][16][17][18][19][20]) or other special class of systems (Delay, Singular, Positive, etc. [21][22][23][24][25][26][27][28][29][30]). Also, numerical consideration for both state feedback and observer design was an important factor specially when dealing with large size systems (see [31][32][33][34]).…”

Section: B Free Design Of Functional Observermentioning

confidence: 99%

Proportional-Integral Observer in Robust Control, Fault Detection, and Decentralized Control of Dynamic Systems

Shafai

Saif

2015

Studies in Systems, Decision and Control

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Abstract. This chapter initially reviews observer theory as it was developed over the past few decades. The state observer and its order reduction including functional observer in connection to state feedback control design are briefly discussed. The robustness of observer-based controller design is also explored. The loss of robustness due to the inclusion of observer in optimal linear quadratic regulator (LQR) and its recovery procedure (LTR) are summarized. The subsequent development of new observer structures such as disturbance observer (DO), unknown input observer (UIO), and proportional-integral observer (PIO) for disturbance estimation and fault detection is highlighted. Throughout the chapter we concentrate mainly on important advantages of PI-observer. Finally, we consider the problem of designing a decentralized PI observer with prescribed degree of convergence for a set of interconnected systems. Under the assumption of linear interactions, we provide a direct design procedure for the PI observer which can effectively be used in disturbance estimation and observer-based control design enhancing the robustness properties. In this connection we also extend the results to the case of designing controllers that attenuate the disturbance while preserving the stability. It is shown that the design can be formulated in terms of LMI which efficiently solve the problem.

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“…[18] and [19] discussed on the existence and synthesis of positive observer. In [19] both the sylvester equation approach and the positive realization approach are presented to investigate the existence and synthesis of positive observer of positive linear systems. Taking into account that it is inevitable that there exist uncertainties in system modeling, an effective approach is further presented to design positive observer for positive systems with parameter uncertainties in [20].…”

Section: Introductionmentioning

confidence: 99%

“…By using a linear programming approach the positive observer was designed in [16] and [17]. [18] and [19] discussed on the existence and synthesis of positive observer. In [19] both the sylvester equation approach and the positive realization approach are presented to investigate the existence and synthesis of positive observer of positive linear systems.…”

Section: Introductionmentioning

confidence: 99%

Positive observer for positive continuous systems with interval uncertainties and multiple time-delay

Wang

Sheng

2012

2012 24th Chinese Control and Decision Conference (CCDC)

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This paper addresses the design of positive observer for positive linear continuous system with interval uncertainties and multiple time-delay. Firstly, the sufficient and necessary condition for the existence of positive observers is established by using the vertical matrices of the uncertain domain which system matrices belong to. Then the desired observer matrices are given by solving a set of matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.Index Terms-ositive observer, time-delay, interval systems, linear matrix inequalities (LMIs), positive systemositive observer, time-delay, interval systems, linear matrix inequalities (LMIs), positive systemp

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Design of Positive Linear Observers for Positive Linear Systems via Coordinate Transformations and Positive Realizations

Cited by 83 publications

References 18 publications

Stabilization of discrete-time LTI positive systems

Stabilization of discrete-time LTI positive systems

Proportional-Integral Observer in Robust Control, Fault Detection, and Decentralized Control of Dynamic Systems

Positive observer for positive continuous systems with interval uncertainties and multiple time-delay

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