Using an Observer to Transform Linear Systems Into Strictly Positive Real Systems

Collado, Joaquı́n; Lozano, Rogelio; Johansson, Rolf

doi:10.1109/tac.2007.899074

Cited by 18 publications

(18 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A design procedure to full-state observers and Lyapunov functions was provided [16]. Modifications of the Kalman-YakubovichPopov Lemma for stabilizable systems using full-order observers were given in [8], [10]. Now, we turn attention to reduced-order observers as instruments in SPR design:…”

Section: Preliminariesmentioning

confidence: 99%

“…(27)-may be summarized as a state-space system where C, D define 47th IEEE CDC, Cancun, Mexico, Dec. [9][10][11]2008 WeB13.2 the output available from the observer-supported system. In this case, we have…”

Section: B Example-output Feedback Of Double-integrator Dynamicsmentioning

confidence: 99%

“…Whereas the proposed method is described for the stable case, it is not detailed for the unstable case though it follows the same outline as for the full-order observer [16], [10]. In the case of stable open-loop systems the method reduces to the introduction of a reduced-order observer and the definition of a new output as a function of the estimated state only.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of stable open-loop systems the method reduces to the introduction of a reduced-order observer and the definition of a new output as a function of the estimated state only. In addition, for the unstable case, we have to introduce observer-state feedback to stabilize the system [16], [10]. The proposed approach does not require the original system to be neither minimum phase nor to have relative degree one.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Strictly positive real systems based on reduced-order observers

Johansson

Collado

Lozano

2008

2008 47th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

We study the extension of the class of linear timeinvariant open-loop systems that may be transformed into SPR systems introducing a reduced-order observer. It is shown that for open-loop stable systems a cascaded observer achieves the result. For open-loop unstable systems observer-based feedback is required to succeed. In general, any stabilizable and observable system may be transformed into an SPR system defining a new output based on the observer state. This overcomes the old conditions of minimum phase and relative degree one for the case of keeping the original output. The result is illustrated with some examples.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Section: B Example-output Feedback Of Double-integrator Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Strictly positive real systems based on reduced-order observers

Johansson

Collado

Lozano

2008

2008 47th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…Estes resultados possuem uma ampla gama de aplicações, como no projeto de sistemas de controle adaptativos (Barkana et al, 2006;Hsu et al, 1994;Huang et al, 1999;Kaufman et al, 1994;Landau, 1979;Owens et al, 1987;Teixeira, 1989), em sistemas de controle com estrutura variável Cardim et al, 2009;Collado et al, 2007;DeCarlo et al, 1988;Shu et al, 2008;Teixeira, 1990;Teixeira, 1993;Teixeira et al, 2000;Teixeira et al, 2002;Teixeira et al, 2006) e na estabilização de sistemas incertos com realimentação da saída (Cunha et al, 2003;Steinberg e Corless, 1985;Xiang et al, 2005).…”

Section: Introductionunclassified

Síntese de Sistemas Estritamente Reais Positivos através do Critério de Routh-Hurwitz

Covacic

Teixeira

Assunção

et al. 2010

Sba Controle & Automação

View full text Add to dashboard Cite

SPR Systems Synthesis Through Routh-Hurwitz CriterionGiven a linear time-invariant plant G ol (s) with one input and q outputs, where q > 1, a method based on the RouthHurwitz Stability Criterion is proposed to obtain a constant tandem matrix F ∈ R q , such that F G ol (s) is a minimumphase system. From this solution, the system F G ol (s) is represented in state space by {A, B, F C} and a constant output feedback matrix K o ∈ R 1 is obtained such that the feedback system {A−BK o C, B, F C} is Strictly Positive Real (SPR). The proposed procedure offers necessary and sufficient conditions for both problems. Initially, the general case, with a generic q, is analyzed. Following, the particular cases q = 2 and q = 3 are studied. RESUMODada uma planta G ol (s) linear e invariante no tempo com uma entrada e q saídas, sendo q > 1, é proposto um método, baseado no Critério de Estabilidade de Routh-Hurwitz, para a obtenção de uma matriz constante F ∈ R q em série com a saída, de modo que o sistema F G ol (s) seja de fase mí-nima. A partir desta solução, o sistema F G ol (s) é representado em espaço de estados por {A, B, F C} e é obtida uma matriz constante de realimentação da saída K o ∈ R 1 , de modo que o sistema realimentado {A − BK o C, B, F C} seja Estritamente Real Positivo (ERP). O procedimento proposto fornece condições necessárias e suficientes para os dois problemas. Inicialmente, é analisado o caso geral, com q gené-rico. Em seguida, são estudados os casos particulares q = 2 e q = 3. PALAVRAS-CHAVE:Sistemas ERP, Fase Mínima, Critério de Routh-Hurwitz, Realimentação da Saída.

show abstract

Robust and Nonlinear Control Literature Survey (No. 2)

2007

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Using an Observer to Transform Linear Systems Into Strictly Positive Real Systems

Cited by 18 publications

References 20 publications

Strictly positive real systems based on reduced-order observers

Strictly positive real systems based on reduced-order observers

Síntese de Sistemas Estritamente Reais Positivos através do Critério de Routh-Hurwitz

Robust and Nonlinear Control Literature Survey (No. 2)

Contact Info

Product

Resources

About