scholarly journals On Minimal Realizations and Minimal Partial Realizations of Linear Time-Invariant Systems Subject to Point Incommensurate Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Linear Time ◽  
Hankel Matrices ◽  
Polynomial Matrices ◽  
Linear Time Invariant ◽  
External Point ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Key Aspects ◽  
Controllability And Observability ◽  
Time Invariant

This paper investigates key aspects of realization and partial realization theories for linear time-invariant systems being subject to a set of incommensurate internal and external point delays. The results are obtained based on the use of formal Laurent expansions whose coefficients are polynomial matrices of appropriate orders and which are also appropriately related to truncated and infinite block Hankel matrices. The above-mentioned polynomial matrices arise in a natural way from the transcendent equations associated with the delayed dynamics. The results are linked to the properties of controllability and observability of dynamic systems. Some related overview is given related to robustness concerned with keeping the realization properties under mismatching between a current transfer matrix and a nominal one.

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.

Enhancing Controllability and Observability in Underactuated and Undersensed Systems Through Switching: Application to Vibration Control

2004 ◽  
Vol 126 (4) ◽  
pp. 790-799 ◽  
Author(s):  
Shahin S. Nudehi ◽  
Ranjan Mukherjee
Keyword(s):  
Dynamical Systems ◽  
Vibration Suppression ◽  
Linear Time ◽  
Flexible Beam ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Controllability And Observability ◽  
Time Invariant ◽  
Control Designs

Many dynamical systems use transducers that can function both as actuators and sensors. It is possible to continuously switch the functionality of the transducer elements in such systems and effectively use each element both as an actuator and a sensor. This provides the scope for significantly reducing the number of transducer elements required for complete controllability and observability of the system and hence reduce the hardware required for controlled system operation. In this paper we advocate underactuation and undersensing in dynamical systems with the objective of reducing cost, weight, and system complexity. To this end, we first illustrate the role of switching in enhancing controllability and observability in underactuated and undersensed linear time-invariant systems and determine the switching requirement for observer-based control designs. For a proof of principle, we consider the problem of vibration suppression in a flexible beam instrumented with piezoelectric transducers. Using simulation and experiments, we demonstrate feasibility of switching the piezoelectric elements between actuator and sensor modalities and establish the merit of introducing underactuation and undersensing deliberately.

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