scholarly journals Minimal realization of an unstable plant under feedback

2021 ◽  
Vol 54 (7) ◽  
pp. 773-778
Author(s):  
Hideyuki Tanaka ◽  
Kenji Ikeda
Keyword(s):  
Minimal Realization ◽  
Unstable Plant

Criteria for Recovery of Zero Initial Condition Responses of Unstable Plants Under Input Saturation

2000 ◽  
Author(s):  
Wei Wu ◽  
Suhada Jayasuriya
Keyword(s):  
Initial Conditions ◽  
Input Saturation ◽  
Input Sequence ◽  
Feedback System ◽  
Open Loop ◽  
Feedback Systems ◽  
Bounded Control ◽  
Analysis And Design ◽  
Study Results ◽  
Unstable Plant

Abstract In this paper, we consider the sufficient and/or necessary conditions under which responses of unstable plants with zero initial conditions would be bounded under step inputs. Several possible unstable pole patterns are examined, and corresponding criteria are derived. It is shown that an unstable plant can be stabilized to have bounded responses using an alternate step input sequence. Step inputs simulate the saturated inputs in a feedback system with bounded control, where the closed-loop stability of an unstable plant is really difficult to study. Results from this open-loop study may lend some insight into the analysis and design of such feedback systems under input saturation nonlinearities.

scholarly journals Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 136
Author(s):  
Manuel Duarte-Mermoud ◽  
Javier Gallegos ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Fractional Order ◽  
Performance Optimization ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Minimal Realization ◽  
Linear Time Invariant ◽  
Mixed Order ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Time Invariant

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

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