Czasopismo | PRZEGLĄD ELEKTROTECHNICZNY | Rocznik 2016 - zeszyt 3

Minimal-phase positive electrical circuits

10.15199/48.2016.03.43

Tadeusz KACZOREK

nr katalogowy: 97035
10.15199/48.2016.03.43

Minimal-phase positive continuous-time linear electrical circuits are addressed. It is shown that positive asymptotically stable electrical circuits with distinct poles and zeros are minimal-phase systems. Conditions are established for electrical circuits to be minimal-phase systems. Sufficient conditions for cancelation of zeros and poles of minimal-phase electrical circuits are proposed. Streszczenie. W pracy są analizowane dodatnie minimalnofazowe obwody elektryczne opisane równaniami stanu i macierzami transmitancji operatorowych. Wykazano, że dodatnie stabilne asymptotycznie obwody elektryczne z różnymi zerami i biegunami są obwodami minimalnofazowymi. Podano warunki minimalnofazowości obwodów elektrycznych, oraz warunki wystarczające upraszczania zer i biegunów w obwodach elektrycznych. Rozważania ogólne zilustrowano przykładami obwodów elektrycznych. (Dodatnie minimalnofazowe obwody elektryczne). Keywords: minimal-phase, positive, asymptotically stable, electrical circuit, pole, zero, cancelation. Słowa kluczowe: minimalnofazowość, dodatniość, stabilność asymptotyczna, obwody elektryczne, zera, bieguny. Introduction In electrical circuits the state variables and outputs take only non-negative values for any non-negative initial conditions and inputs. The positive standard and fractional order electrical circuits have been investigated in many papers and books [1-7]. A new class of normal electrical circuits has been introduced in [8]. The minimum energy control of electrical circuits has been investigated in [9]. Positive linear systems consisting of n subsystems with different fractional orders have been addressed in [10, 11]. Decoupling zeros of positive linear systems have been introduced in [12]. Determination of the state space equations for given transfer matrices is a classical problem, called the realization problem, which has been addressed in many papers and books [13-17]. An overview of the positive realization [...]

Bibliografia

[1] Kaczorek T. , A class of positive and stable time-varying electrical circuits. Electrical Review, vol. 91, no. 5, (2015), 121-124.
[2] Kaczorek T. , Constructability and observability of standard and positive electrical circuits. Electrical Review, vol. 89, no. 7, (2013), 132-136.
[3] Kaczorek T., Rogowski K., Fractional Linear Systems and Electrical Circuits. Studies in Systems, Decision and Control, vol. 13, Springer,(2015).
[4] Kaczorek T. , Positive electrical circuits and their reachability. Archives of Electrical Engineering, vol. 60, no. 3, (2011), 283-301.
[5] Kaczorek T. , Positive fractional linear electrical circuits. Proceedings of SPIE, vol. 8903, Bellingham WA, USA, Art. No 3903-35.
[6] Kaczorek T. , Positive unstable electrical circuits. Electrical Review, vol. 88, no. 5a, (2012), 187-192.
[7] Kaczorek T. , Zeroing of state variables in descriptor electrical circuits by state-feedbacks. Electrical Review, vol. 89, no. 10, (2013), 200-203.
[8] Kaczorek T. , Normal positive electrical circuits. IET Circuits Theory and Applications, vol. 9, no. 5, (2015), 691-699.
[9] Kaczorek T. , Minimum energy control of positive electrical circuits. Proc. of Conf. MMAR, Miedzyzdroje, Aug. 2-5, (2014), 2-9.
[10] Kaczorek T. , Positive linear systems with different fractional orders. Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, (2010), 453-458.
[11] Kaczorek T. , Positive systems consisting of n subsystems with different fractional orders. IEEE Trans. Circuits and PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 92 NR 3/2016 189 Systems - regular paper, vol. 58, no. 6, June (2011), 1203- 1210.
[12] Kaczorek T. , Decoupling zeros of positive continuous-time linear systems and electrical circuits. Advances in Systems Science. Advances in Intelligent Systems and Computing, vol. 240, (2014), Springer, 1-15.
[13] L. , Far ina L. , A tutorial on the positive realization problem. IEEE Trans. on Automatic Control, vol. 49, no. 5, (2004), 651- 664.
[14] Far ina L. , Rinaldi S. , Positive Linear Systems; Theory and Applications. J. Wiley, New York, (2000).
[15] Kaczorek T. , Linear Control Systems, vol. 1. Research Studies Press, J. Wiley, New York, (1992).
[16] Kaczorek T . , Sajewsk i Ł . , The Realization Problem for Positive and Fractional Systems, Springer, Heidelberg, (2014).
[17] Shaked U. , Di xon M. , Generalized minimal realization of transfer-function matrices. Int. J. Contr., vol. 25, no. 5, (1977), 785-803.
[18] Kaczorek T. , Positive 1D and 2D Systems. Springer- Verlag, London, (2002).
[19] Kaczorek T. , A realization problem for positive continuoustime linear systems with reduced numbers of delays. Int. J. Appl. Math. Comput. Sci., vol. 16, no. 3, (2006), 325-331.
[20] Kaczorek T. , Computation of positive stable realizations for discrete-time linear systems. Computational Problems of Electrical Engineering, vol. 2, no. 1, (2012), 41-48.
[21] Kaczorek T. , Computation of positive stable realizations for linear continuous-time systems. Bull. Pol. Acad. Techn. Sci., vol. 59, no. 3, (2011), 273-281.
[22] Kaczorek T. , Computation of realizations of discrete-time cone systems. Bull. Pol. Acad. Sci. Techn., vol. 54, no. 3, (2006), 347-350.
[23] Kaczorek T. , Positive and asymptotically stable realizations for descriptor discrete-time linear systems. Bull. Pol. Acad. Sci. Techn., vol. 61, no. 1, (2013), 229-237.
[24] Kaczorek T. , Positive minimal realizations for singular discrete-time systems with delays in state and delays in control. Bull. Pol. Acad. Sci. Techn., vol. 53, no. 3, (2005), 293-298.
[25] Kaczorek T. , Positive stable realizations of discrete-time linear systems. Bull. Pol. Acad. Sci. Techn., vol. 60, no. 3, (2012), 605-616.
[26] Kaczorek T. , Positive stable realizations with system Metzler matrices. Archives of Control Sciences, vol. 21, no. 2, (2011), 167-188.
[27] Kaczorek T. , Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. Int. J. Appl. Math. Comput. Sci., vol. 16, no. 2, (2006), 101-106.
[28] Kaczorek T. , Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems. Archives of Control Sciences, vol. 22, no. 4, (2012), 371-384.
[29] Kaczorek T. , Positive realizations with reduced numbers of delays for 2-D continuous-discrete linear systems. Bull. Pol. Acad. Sci. Techn., vol. 60, no. 4, (2012), 835-840.
[30] Kaczorek T. , Positive stable realizations for fractional descriptor continuous-time linear systems. Archives of Control Sciences, vol. 22, no. 3, (2012), 255-265.
[31] Kaczorek T. , Positive stable realizations of fractional continuous-time linear systems. Int. J. Appl. Math. Comput. Sci., vol. 21, no. 4, (2011), 697-702.
[32] Kaczorek T. , Realization problem for fractional continuoustime systems. Archives of Control Sciences, vol. 18, no. 1, (2008), 43-58.
[33] Sajewski Ł . , Positive stable minimal realization of fractional discrete-time linear systems, Advances in the Theory and Applications of Non-integer Order Systems Eds. W. Mitkowski et al., Springer, 257, (2013), 15-30.
[34] Sajewski Ł . , Positive stable realization of fractional discrete-time linear systems, Asian Journal of Control, 16 (3), DOI: 10.1002/asjc.750, (2014).
[35] Sajewski Ł . , Positive realization of fractional continuoustime linear systems with delays, Measurement Automation and Monitoring, 58 (5) , (2012), 413-417.
[36] Sajewski Ł . , Positive realization of fractional discrete-time linear systems with delays, Pomiary Automatyka Robotyka, 2, CD-ROM, (2012).
[37] Kaczorek T. , A modified state variables diagram method for determination of positive realizations of linear continuoustime systems with delays. Int. J. Appl. Math. Comput. Sci., vol. 22, no. 4, (2012), 897-905.
[38] Kaczorek T. , Minimal-phase realizations for positive linear systems, Technika Transportu Szynowego, vol.12 (2015).

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