Design of linear functional observers for linear systems with unknown inputs

Trinh, Hieu; Ha, Q.P.

doi:10.1080/00207720050030789

Cited by 45 publications

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“…This problem was solved in [13], where the reconstruction problem for a linear functional σ = F x, F ∈ R q×n , was considered, where q is the dimension of the control u(t). (This assumption does not restrict the generality of considerations.…”

Section: Elimination Of Perturbation From the Equation For The Estimamentioning

confidence: 99%

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Observers for Linear Dynamical Systems with Indeterminacy

et al. 2005

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Section: Elimination Of Perturbation From the Equation For The Estimamentioning

confidence: 99%

“…A procedure for solving system (28) with an arbitrary stable matrix E and the proof of the solvability of this system were given in [13] but only for the case in which…”

Section: The Estimation Error E(t) = Z(t) − X (T) Satisfies the Equatioṅmentioning

confidence: 99%

Observers for Linear Dynamical Systems with Indeterminacy

et al. 2005

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“…The observer synthesis problem for indeterminate systems was considered in a number of papers (e.g., see [2][3][4][5][6], where sufficient conditions for the existence of asymptotic observers were described and algorithms for their synthesis were suggested). 1 The main results of the present paper were announced in the journal Doklady RAN (…”

Section: Statement Of the Problemmentioning

confidence: 99%

Synthesis of asymptotic observers for linear vector indeterminate systems

et al. 2005

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STATEMENT OF THE PROBLEMIn classical control theory, the construction of observers, that is, dynamical systems that provide an asymptotic estimate of the system phase vector on the basis of information about a known output of the system, is one of the key problems. This problem is especially complicated and important if the information about the characteristics of the system or the perturbations is incomplete.Consider the statement of this problem more rigorously. Consider the dynamical systeṁwhere A ∈ R n×n , B ∈ R n×m , and C ∈ R l×n are known matrices with constant coefficients, u(t) ∈ R m is a known input of the system (the control), y(t) ∈ R l is a measurable output of the system, and f (t, x) ∈ R m is an unknown perturbation (an input signal or a deviation of parameters). For given input u(t) and output y(t), the task is to obtain an asymptotic estimatex(t) of the state vector x(t).We assume that the pair {A, B} is controllable and the pair {C, A} is observable, i.e., system (1) is in general position. This problem has been comprehensively studied for the case in which the perturbation f (t, x) is absent (e.g., see [1]). It is known that this problem is solved by the full-dimensional observeṙwhere the matrix L ∈ R n×l is chosen from the stability condition for the systeṁ e = (A − LC)e = A L e for the deviations e =x − x. Since the pair {C, A} is observable, it follows that the matrix L completely determines the spectrum of the matrix A L , and the observer (2) solves the problem exponentially with an arbitrarily prescribed convergence rate. Furthermore, for an indeterminacy-free system [i.e., for f (t, x) ≡ 0], one can construct a Luenberger observer of lower order n − l. A detailed exposition of observer synthesis methods for such systems can be found in numerous papers (e.g., see [1]).The situation is rather different if the system contains an indeterminacy f (t, x). In this case, the system in deviations has the formėand if the noise f (t, x) is nonvanishing, then the observer (2) does not necessarily provide an asymptotic estimate of the vector x(t).The observer synthesis problem for indeterminate systems was considered in a number of papers (e.g., see [2][3][4][5][6], where sufficient conditions for the existence of asymptotic observers were described and algorithms for their synthesis were suggested). 1 The main results of the present paper were announced in the journal Doklady RAN (

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“…The design of linear functional observers has been the focus of many researchers over the years. A number of procedures have been proposed for the design of linear functional state observers (see for example Sirisena (1979), Fairman and Gupta (1980), O'Reilly (1983), Tsui (1986), Trinh (1999) and Trinh and Ha (2000)). Although linear functional observers have been developed for multivariable systems (Darouach 2000), little research has focused on their use, in a decentralized way, for multi-agent systems.…”

Section: Introductionmentioning

confidence: 99%

Observer-based control of multi-agent systems under decentralized information structure

Trinh

2004

International Journal of Systems Science

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This paper addresses the problem of decentralized implementation of a global state feedback controller for multi-agent systems. The system is assumed to be under the constraint of a complete decentralized information structure. The decentralization of the control task is achieved through the construction of low-order decentralized functional observers with the purpose of generating the required corresponding control signal for each local control station. A design procedure is developed for obtaining an approximate solution to the design of the observers. Stability analysis is provided for the global system using the proposed observer-based approach. A numerical example is given to illustrate the design procedure and cases when the observers' order increases from the lowest value.

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Design of linear functional observers for linear systems with unknown inputs

Cited by 45 publications

References 0 publications

Observers for Linear Dynamical Systems with Indeterminacy

Observers for Linear Dynamical Systems with Indeterminacy

Synthesis of asymptotic observers for linear vector indeterminate systems

Observer-based control of multi-agent systems under decentralized information structure

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