Design of minimal order stable observers for linear functions of the state via realization theory

Roman, J.R.; Bullock, T. E.

doi:10.1109/tac.1975.1101061

Cited by 71 publications

(11 citation statements)

References 21 publications

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“…In this section, we investigate the functional observer and state feedback designs by the state space approach shown in Figure 1 and the equations (2), (3 1 ), (4') and the transfer fuaction approach shown in Figure 2 and the equation (6).…”

Section: Functional Observer and State Feedbackmentioning

confidence: 99%

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Functional observer and state feedback

Zhang

1987

International Journal of Control

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In this paper, we show the relation between state space approach and transfer function approach for functional observer and state feedback design. Two approaches can be transformed into each other, based on this result. More importantly, we find that th= scate space approach introduces some severe, unnecessary restrictions in solving the problem. The restrictions are, however, reduced to be a trivial condition in transfer function approach. It is believed that the result presented in this paper will be useful in developing both approaches, and motivate some new results for solving the problem.

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Section: Functional Observer and State Feedbackmentioning

confidence: 99%

“…The following example is shown to illustrate the result of section V. We solve the functional observer and state feedback problem by transfer function approach (6). Then, by using the realization of section IV.…”

Section: Examplementioning

confidence: 99%

Functional observer and state feedback

Zhang

1987

International Journal of Control

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“…Much of the early work dating back to the work of Luenberger on functional observers has focused on the existence and design of minimum-order functional observers (see Fortmann & Williamson, 1972;Furuta & Kawaji, 1977;Gupta, Fairman, & Hinamoto, 1981;Moore & Ledwich, 1975;O'Reilly, 1983;Roman & Bullock, 1975;Sirisena, 1979;Trinh, 1999). Some early studies on the reduction of the order of functional observers were also reported in Tsui (1985Tsui ( , 1986).…”

Section: Introductionmentioning

confidence: 99%

A system decomposition approach to the design of functional observers

Fernando

Trinh

2014

International Journal of Control

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This paper reports a system decomposition that allows the construction of a minimum-order functional observer using a state observer design approach. The system decomposition translates the functional observer design problem to that of a state observer for a smaller decomposed subsystem. Functional observability indices are introduced, and a closed-form expression for the minimum order required for a functional observer is derived in terms of those functional observability indices. IntroductionLinear functional observers estimate linear functions of the state vector of a system without estimating all the individual states. The idea of an observer to directly estimate a linear function of the state vector was initially suggested by Luenberger (1966). This concept of a functional observer was introduced in the context of designing a low-order observer to estimate a desired linear function or functions of the state vector. Functional observers can play an important role in state feedback controller implementation because a control law can be directly estimated from input and output data using a functional observer. The main advantage of employing a functional observer lies in its ability to directly estimate a given linear function of the state vector without having to estimate all the individual states. The direct estimation of a linear function allows the observer structure to have minimal dimension, always a smaller order than a fullorder state observer, and also always an order less than or equal to the reduced-order Luenberger observer. Designing the simplest possible order observer to estimate a given linear function from a practical point of view allows its implementation with the least possible components. This salient feature of possible reduced order for a functional observer has motivated researchers around the world to find ways to systematically design minimum-order functional observers since the concept was first introduced by Luenberger.Intuitively, reduced order that is possible for a functional observer points to estimating states of a subsystem only, and not the states of the entire system. This paper explores the idea of estimating only the states of a subsystem in order to obtain the desired functional estimates, and to this end, reports a system decomposition approach.

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“…As one of the effective state estimation methods, the design of observers which estimate linear functions of the state vector, in short functional observers, were first studied in [3]. Since then, many other approaches have been developed to design linear functional observers [4][5][6][7][8][9] on the condition that the estimation error converges to zero in an asymptotically fashion.…”

Section: Introductionmentioning

confidence: 99%

Design of parametric finite time functional observers in linear time-invariant systems

Wang¹,

Lv²,

Lu³

2012

Proceedings of the 10th World Congress on Intelligent Control and Automation

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A design problem of the parametric finite time functional observers in the linear time-invariant systems is investigated. The aim is to design the parametric form of the functional observers which can estimate directly the linear functions of the state for the linear time-invariant systems in a predefined finite time. Based on the parametric solutions for a class of Sylvester matrix equation, this paper presents the parametric expressions of all the gain matrices for the finite time functional observers, in which the free parameters can offer all the design degrees of freedom for control system design. Finally, a numerical example and its simulation results show the simplicity and effectiveness of the proposed design method of parametric finite time functional observers in the linear timeinvariant systems.

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Design of minimal order stable observers for linear functions of the state via realization theory

Cited by 71 publications

References 21 publications

Functional observer and state feedback

Functional observer and state feedback

A system decomposition approach to the design of functional observers

Design of parametric finite time functional observers in linear time-invariant systems

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