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Properties of Eventually Positive Linear Input-Output Systems [article]

Aivar Sootla
2016 arXiv   pre-print
We then extend the notion of eventually positive systems to the input-output system case.  ...  Our extension is performed in such a manner, that some valuable properties of classical internally positive input-output systems are preserved.  ...  We then define an input-output analogue of the eventually positive systems and show that these systems possess some properties of internally positive systems, as well.  ... 
arXiv:1509.08392v2 fatcat:tsvfhqkaefav3pfiuyxkno53zq

On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays

Manuel De la Sen
2022 Systems  
The property of external positivity of dynamic systems is commonly defined as the non-negativity of the output for all time under zero initial conditions and any given non-negative input for all time.  ...  This paper investigates the extension of that property for a structured class of initial conditions of a single-input single-output (SISO) linear dynamic system which can include, in general, certain negative  ...  Conflicts of Interest: The author declares no conflict of interests.  ... 
doi:10.3390/systems10010009 fatcat:fv4rxctw3vbmvj7xkymuvuwatu

About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma

M. De la Sen
2017 Discrete Dynamics in Nature and Society  
The hyperstability and asymptotic hyperstability properties of the studied class of positive hybrid systems under feedback from any member of a nonlinear (and, eventually, time-varying) class of controllers  ...  This paper formulates an "ad hoc" robust version under parametrical disturbances of the discrete version of the Kalman-Yakubovich-Popov Lemma for a class of positive hybrid dynamic linear systems which  ...  Acknowledgments The author is very grateful to the Spanish Government and European Fund of Regional Development FEDER for Grant DPI2015-64766-R and to UPV/EHU by its Grant PGC 17733 for research groups  ... 
doi:10.1155/2017/3928970 fatcat:g35veiwdavaedgxtxfjyhmdzyq

Aspects and Some Results on Passivity and Positivity of Dynamic Systems

M. De la Sen
2017 Journal of Physics, Conference Series  
, by adding a positive parallel direct input-output matrix interconnection gain.  ...  In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity and very strict passivity (i.e. joint strict input and output passivity) are given  ...  Acknowledgements This research is supported by the Spanish Government and by the European Fund of Regional Development FEDER through Grant DPI2015-64766-R and by UPV/EHU by Grant PGC 17/33.  ... 
doi:10.1088/1742-6596/936/1/012099 fatcat:dhs5aus3rrfrholcef73ruf66m

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov's Inequality

M. De la Sen
2018 Mathematical Problems in Engineering  
This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging  ...  is strictly positive real.  ...  Acknowledgments The author is very grateful to the Spanish Government and European Fund of Regional Development FEDER for Grant no.  ... 
doi:10.1155/2018/7861396 fatcat:7xc7nd5skzhxrockly2vi3f4vi

Page 527 of Mathematical Reviews Vol. , Issue 93a [page]

1993 Mathematical Reviews  
It is shown that the existence of a solution to the corresponding set of equations and inequalities depends on the structural properties of an associated input-output system (the number of system zeros  ...  Feintuch [Linear Algebra Appl. 122/123/124 (1989), 105-114; MR 91a:93051], the notion of an eventually time-invariant system was defined.  ... 

Output-input stability and minimum-phase nonlinear systems

D. Liberzon, A.S. Morse, E.D. Sontag
2002 IEEE Transactions on Automatic Control  
This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems.  ...  The class of output-input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose  ...  Loosely speaking, we will call a system output-input stable if its state and input eventually become small when the output and derivatives of the output are small.  ... 
doi:10.1109/9.989070 fatcat:luwuhhdyijbw7essxiwerlihie

From vehicular platoons to general networked systems: String stability and related concepts

S. Stüdli, M.M. Seron, R.H. Middleton
2017 Annual Reviews in Control  
In some cases the use of heterogeneous controllers is even suggested to improve the performance of the system (Khatir and Davidson, 2004) .  ...  A second goal is to extend the definitions to general networked systems. The use of homogeneous agents simplifies the analysis, however idealises the systems dramatically.  ...  Also, these are mostly modeled as single input, single output systems, where the input is commonly a positional error and the output is the position of the vehicle.  ... 
doi:10.1016/j.arcontrol.2017.09.016 fatcat:k7mf7frlzba3tpxwqbfvudx3iu

On the Design of Hyperstable Feedback Controllers for a Class of Parameterized Nonlinearities. Two Application Examples for Controlling Epidemic Models

Manuel De la Sen
2019 International Journal of Environmental Research and Public Health  
This paper studies the hyperstability and the asymptotic hyperstability of a single-input single-output controlled dynamic system whose feed-forward input-output dynamics is nonlinear and eventually time-varying  ...  In this way, set of robust hyperstability and asymptotic hyperstability of the closed-loop system are given based on the fact that the input-output energy of the feed-forward controlled system is positive  ...  Conflicts of Interest: The author declares no conflict of interest.  ... 
doi:10.3390/ijerph16152689 pmid:31357623 pmcid:PMC6696007 fatcat:qyn4zctf2neyxptw5i3kz2vike

A Class of Quasi-Natural Potentials and Hyper-Stable PID Servo-Loops for Nonlinear Robotic Systems

Suguru ARIMOTO
1994 Transactions of the Society of Instrument and Control Engineers  
joint trajectories satisfy the passivity with respect to the residual input torque and a linear sum of residual velocity and saturated residual position outputs.  ...  It is further shown that in the case of trajectory tracking the passivity of residual robot dynamics with SP-D feedback loops plays a vital role and eventually leads to the adaptability in model-based  ...  and an output as a linear combination of the velocities and saturated positional differences.  ... 
doi:10.9746/sicetr1965.30.1005 fatcat:thszganntzgk7cx3lruakjzduy

Network Systems and String Stability [article]

S. Stuedli, M. M. Seron, R. H. Middleton
2017 arXiv   pre-print
Network systems and their control are highly important and appear in a variety of applications, including vehicle platooning and formation con- trol.  ...  A second goal is to generalise the found definitions for general network systems.  ...  outputs of the networked system H(s).  ... 
arXiv:1702.05826v1 fatcat:pfg3a3c4ivewbmvgjm726bn2tu

A Fuzzy Adaptive GPS/INS Integrated Navigation Algorithm

Mingwei Liu, Fenfen Xiong
2011 Procedia Engineering  
The statistical properties of the measurement noise of the missile-borne navigation system would vary under different actual working conditions.  ...  Thus the Kalman filter can be adjusted to the optimal state, which eventually improves the accuracy of the integrated navigation system.  ...  Acknowledgements The grant supports from National Natural Science Foundation of China (NO. 10972034) and Posterdoctoral Science Foundation of China (NO. 20100470213) are greatly acknowledged.  ... 
doi:10.1016/j.proeng.2011.08.123 fatcat:kvwx5hqqkrggfgg7ljrjps4ihi

About robust hyperstability and dissipativity of linear time-invariant dynamic systems subject to hyperstable controllers and unstructured delayed state and output disturbances

M. De la Sen, Bin Zhou
2018 Cogent Engineering  
or not since the properties depend only of the measured input and output.  ...  the sate and output.  ...  Acknowledgements The author is very grateful to the Spanish Government and European Fund of Regional Development FEDER for Grant DPI2015-64766-R and to the UPV/EHU by its support via Grant PGC 17/33.  ... 
doi:10.1080/23311916.2018.1437662 fatcat:kwe37hoogzaubmjledkqxh5j6a

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

M. De la Sen
2013 Abstract and Applied Analysis  
The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers.  ...  asymptotic hyperstability of dynamic systems are discussed later on.  ...  Acknowledgments The author is very grateful to the Spanish Government for its support of this research through Grant DPI2012-30651 and to the Basque Government for its support of this research through  ... 
doi:10.1155/2013/639576 fatcat:qlvptd4r3ne5hfh7t67pzbbzke

On the global limits and oscillations of a system of nonlinear differential equations describing a flow on a probabilistic network

Stephen Grossberg
1969 Journal of Differential Equations  
subjected to inputs Z = (I1 , I, , Z,) by an experimenter d who records the outputs X = (x1 , x2, xa) created thereby. 8 has only the inputs Z and the outputs X at his disposal with which to describe (  ...  =l (1) where i, j, k = 1,2, 3 and /3 is a positive number.  ...  Also this alternative does not correspond to an alternative between linearity and nonlinearity of the system, since in both cases the system is eventually linear. OUTPUT SIZE vs.  ... 
doi:10.1016/0022-0396(69)90092-8 fatcat:fct5gjiqk5ambitisqlavvkaue
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