Robust Stability Analysis of Distributed-Order Linear Time-Invariant Systems With Uncertain Order Weight Functions and Uncertain Dynamic Matrices

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Hamed Taghavian ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Weight Function ◽  
Robust Stability ◽  
Linear Time ◽  
Upper And Lower Bounds ◽  
Weight Functions ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Robust Stability Analysis ◽  
Time Invariant ◽  
Distributed Order

Bounded-input bounded-output (BIBO) stability of distributed-order linear time-invariant (LTI) systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties, it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex plane defined by the upper and lower bounds of the order weight function. Thereby, sufficient conditions are obtained to ensure robust stability in distributed-order LTI systems with uncertain order weight functions and uncertain dynamic matrices. Numerical examples are presented to verify the obtained results.

scholarly journals Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Radek Matušů ◽  
Bilal Şenol ◽  
Libor Pekař
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
Linear Time ◽  
Parametric Uncertainty ◽  
Uncertainty Modeling ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Robust Stability Analysis ◽  
Uncertainty Models ◽  
Time Invariant

The main aim of this paper is to present and compare three approaches to uncertainty modeling and robust stability analysis for fractional-order (FO) linear time-invariant (LTI) single-input single-output (SISO) uncertain systems. The investigated objects are described either via FO models with parametric uncertainty, by means of FO unstructured multiplicative uncertainty models, or through FO unstructured additive uncertainty models, while the unstructured models are constructed on the basis of appropriate selection of a nominal plant and a weight function. Robust stability investigation for systems with parametric uncertainty uses the combination of plotting the value sets and application of the zero exclusion condition. For the case of systems with unstructured uncertainty, the graphical interpretation of the utilized robust stability test is based mainly on the envelopes of the Nyquist diagrams. The theoretical foundations are followed by two extensive, illustrative examples where the plant models are created; the robust stability of feedback control loops is analyzed, and obtained results are discussed.

scholarly journals Tuning of a time-delayed controller for a general class of second-order linear time invariant systems with dead-time

2019 ◽  
Vol 13 (3) ◽  
pp. 451-457 ◽  
Author(s):  
Raul Villafuerte-Segura ◽  
Francisco Medina-Dorantes ◽  
Leopoldo Vite-Hernández ◽  
Baltazar Aguirre-Hernández
Keyword(s):  
General Class ◽  
Dead Time ◽  
Linear Time ◽  
Second Order ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

scholarly journals Balanced truncation of linear time-invariant systems over finite-frequency ranges

2020 ◽  
Vol 46 (6) ◽  
Author(s):  
Peter Benner ◽  
Xin Du ◽  
Guanghong Yang ◽  
Dan Ye
Keyword(s):  
Error Bounds ◽  
Linear Time ◽  
Upper And Lower Bounds ◽  
Single Frequency ◽  
Frequency Interval ◽  
Balanced Truncation ◽  
Frequency Dependent ◽  
Linear Time Invariant ◽  
Type Frequency ◽  
Time Invariant

AbstractThis paper discusses model order reduction of linear time-invariant (LTI) systems over limited frequency intervals within the framework of balanced truncation. Two new frequency-dependent balanced truncation methods are developed, one is single-frequency (SF)-type frequency-dependent balanced truncation to cope with the cases that only a single dominating point of the operating frequency interval is pre-known, and the other is interval-type frequency-dependent balanced truncation to deal with the case that both the upper and lower bounds of the relevant frequency interval are known a priori. Error bounds for both approaches are derived to estimate the approximation error over a pre-specified frequency interval. In contrast to other error bounds for frequency-weighted or frequency-limited balanced truncation, these bounds are given specifically for the interval under consideration and are thus often sharper than the global bounds for previous methods. We show that the new methods generally lead to good in-band approximation performance, and at the same time provide accurate error bounds under certain conditions. Examples are included for illustration.

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