3,827 research outputs found
Positivity of Continuous-Time Descriptor Systems With Time Delays
This technical note is concerned with positivity characteristic of continuous-time descriptor systems with time delays. First, a set of necessary and sufficient conditions is presented to check the property. Then, considering a descriptor time-delay system with two assumptions, a new time-delay system is established whose positivity is equivalent to that of the original system. Furthermore, a set of necessary and sufficient conditions is provided to check the positivity of the new system. Finally, a numerical example is given to illustrate the validity of the results obtained
Stability of fractional order systems
The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled
Bounded real lemmas for positive descriptor systems
A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs). In this paper, based on the positivity characterization, a novel bounded real lemma for continuous positive descriptor systems in terms of strict LMI is first established by the separating hyperplane theorem. The result developed here provides a necessary and sufficient condition for systems to possess H?H? norm less than ? and shows the existence of PDDM solution. Moreover, under certain condition, a simple model reduction method is introduced, which can preserve positivity, stability and H?H? norm of the original systems. An advantage of such method is that systems? matrices of the reduced order systems do not involve solving of LMIs conditions. Then, the obtained results are extended to discrete case. Finally, a numerical example is given to illustrate the effectiveness of the obtained results
Non-Lyapunov stability of the fractional-order time-varying delay systems
U ovom radu, kriterijumi stabilnosti na konaÄnom vremenskom intervalu su proĆĄireni na nelinearne nehomogene perturbovane sisteme necelobrojnog reda koji sadrĆŸe viĆĄestruka vremenski promenljiva kaĆĄnjenja. Dobijeni su dovoljni uslovi stabilnosti za sisteme necelog reda sa viĆĄestrukim vremenskim kaĆĄnjenjima koriĆĄÄenjem generalizovanog i klasiÄnog Gronwallovog pristupa. NumeriÄki primer je dat u cilju ilustracije znaÄaja dobijenog rezultata.In this paper, the finite-time stability criteria are extended to nonlinear nonhomogeneous perturbed fractional-order systems including multiple time-varying delays. The sufficient conditions of a stability for the fractional systems with multiple time delays are obtained by using the generalized and classical Gronwall's approach. A numerical example is presented to illustrate the validity of the obtained result
Non-Lyapunov stability of the fractional-order time-varying delay systems
U ovom radu, kriterijumi stabilnosti na konaÄnom vremenskom intervalu su proĆĄireni na nelinearne nehomogene perturbovane sisteme necelobrojnog reda koji sadrĆŸe viĆĄestruka vremenski promenljiva kaĆĄnjenja. Dobijeni su dovoljni uslovi stabilnosti za sisteme necelog reda sa viĆĄestrukim vremenskim kaĆĄnjenjima koriĆĄÄenjem generalizovanog i klasiÄnog Gronwallovog pristupa. NumeriÄki primer je dat u cilju ilustracije znaÄaja dobijenog rezultata.In this paper, the finite-time stability criteria are extended to nonlinear nonhomogeneous perturbed fractional-order systems including multiple time-varying delays. The sufficient conditions of a stability for the fractional systems with multiple time delays are obtained by using the generalized and classical Gronwall's approach. A numerical example is presented to illustrate the validity of the obtained result
Uniform bounded input bounded output stability of fractionalâorder delay nonlinear systems with input
The bounded input bounded output (BIBO) stability for a nonlinear Caputo
fractional system with time-varying bounded delay and nonlinear output is
studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input
bounded output stability criteria are derived. Also, explicit and independent on
the initial time bounds of the output are provided. Uniform BIBO stability and
uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the systemâs dynamic response, and demonstrate the
effectiveness of our theoretical results.publishe
Emerging applications of integrated optical microcombs for analogue RF and microwave photonic signal processing
We review new applications of integrated microcombs in RF and microwave
photonic systems. We demonstrate a wide range of powerful functions including a
photonic intensity high order and fractional differentiators, optical true time
delays, advanced filters, RF channelizer and other functions, based on a Kerr
optical comb generated by a compact integrated microring resonator, or
microcomb. The microcomb is CMOS compatible and contains a large number of comb
lines, which can serve as a high performance multiwavelength source for the
transversal filter, thus greatly reduce the cost, size, and complexity of the
system. The operation principle of these functions is theoretically analyzed,
and experimental demonstrations are presented.Comment: 16 pages, 8 figures, 136 References. Photonics West 2018 invited
paper, expanded version. arXiv admin note: substantial text overlap with
arXiv:1710.00678, arXiv:1710.0861
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