Design of Minimal-Order Observer for Singular Systems

Shafai, B.; Carroll, Robert L.

doi:10.23919/acc.1986.4789273

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…It follows from (9) that rank       E C 12 = n, then the general solution of (11) is therefore given by…”

Section: Reduced-order Observer Designmentioning

confidence: 99%

“…A procedure to compute efficiently the observer matrices can be obtained from the singular values decomposition of the full column matrices (ϕ F 12 ) and       E C 12 . This problem has not been presented in this paper, the reader can refer to [8] for more details on the computations problems.…”

Section: Lemma 33 Under the Assumption Rankmentioning

confidence: 99%

“…In [11] the generalized Sylvester equation was used to develop a procedure for designing reduced-order observers. In [12] a method based on the generalized inverse was presented. Observers for continuous descriptor under less restrictive conditions and using only a straightforward matrix manipulation have been presented in [17], [18].…”

Section: Introductionmentioning

confidence: 99%

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Reduced-order observer design for descriptor systems with unknown inputs

Darouach¹,

Zasadzinski²,

Hayar³

1996

IEEE Trans. Automat. Contr.

190

127

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“…It follows from (9) that rank       E C 12 = n, then the general solution of (11) is therefore given by…”

Section: Reduced-order Observer Designmentioning

confidence: 99%

Section: Lemma 33 Under the Assumption Rankmentioning

confidence: 99%

See 1 more Smart Citation

Reduced-order observer design for descriptor systems with unknown inputs

Darouach¹,

Zasadzinski²,

Hayar³

1996

IEEE Trans. Automat. Contr.

190

127

View full text Add to dashboard Cite

show abstract

“…Now partitioning T ∈ R r×n as T 1 T 2 , where T 1 ∈ R r×p and T 2 ∈ R r×(n−p) , and substituting it along with partitioned pair {A, C} defined by (25) in (33) leads to…”

Section: F ∈ R R×rmentioning

confidence: 99%

“…Let us consider a system represented in output identifiable form with the pair {A, C} defined by (25). We provide a method of designing a single functional observer with desired eigenvalues to estimate w = kx, where k is a given 1 × n constant vector.…”

Section: A Fixed 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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