메뉴 건너뛰기




Volumn 52, Issue 3, 2014, Pages 1809-1831

Stability analysis of positive semi-Markovian jump linear systems with state resets

Author keywords

Markovian renewal processes; Mean stability; Positive systems; Semi Markovian jump linear systems

Indexed keywords

LINEAR SYSTEMS; MATRIX ALGEBRA;

EID: 84905019957     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/130925177     Document Type: Article
Times cited : (58)

References (40)
  • 1
    • 84879679480 scopus 로고    scopus 로고
    • Stochastic hybrid systems with renewal transitions: Moment analysis with application to networked control systems with delays
    • D. ANTUNES, J. P. HESPANHA, AND C. SILVESTRE, Stochastic hybrid systems with renewal transitions: Moment analysis with application to networked control systems with delays, SIAM J. Control Optim., 51(2013), pp. 1481-1499.
    • (2013) SIAM J. Control Optim. , vol.51 , pp. 1481-1499
    • Antunes, D.1    Hespanha, J.P.2    Silvestre, C.3
  • 2
    • 0001020392 scopus 로고
    • Method of power transformations for analysis of stability of nonlinear control systems
    • A. BARKIN AND A. ZELENTSOVSKY, Method of power transformations for analysis of stability of nonlinear control systems, Systems Control Lett., 3(1983), pp. 303-310.
    • (1983) Systems Control Lett. , vol.3 , pp. 303-310
    • Barkin, A.1    Zelentsovsky, A.2
  • 3
    • 84870429995 scopus 로고    scopus 로고
    • Co-positive Lyapunov functions for the stabilization of positive switched systems
    • F. BLANCHINI, P. COLANERI, AND M. E. VALCHER, Co-positive Lyapunov functions for the stabilization of positive switched systems, IEEE Trans. Automat. Control, 57(2012), pp. 3038-3050.
    • (2012) IEEE Trans. Automat. Control , vol.57 , pp. 3038-3050
    • Blanchini, F.1    Colaneri, P.2    Valcher, M.E.3
  • 4
    • 77953135017 scopus 로고    scopus 로고
    • Markov Jump Linear Systems with switching transition rates: Mean square stability with dwell-time
    • P. BOLZERN, P. COLANERI, AND G. DE NICOLAO, Markov Jump Linear Systems with switching transition rates: Mean square stability with dwell-time, Automat., 46(2010), pp. 1081-1088.
    • (2010) Automat. , vol.46 , pp. 1081-1088
    • Bolzern, P.1    Colaneri, P.2    De Nicolao, G.3
  • 6
    • 0018011435 scopus 로고
    • Kronecker products and matrix calculus in system theory
    • J. BREWER, Kronecker products and matrix calculus in system theory, IEEE Trans. Circuits Systems, 25(1978), pp. 772-781.
    • (1978) IEEE Trans. Circuits Systems , vol.25 , pp. 772-781
    • Brewer, J.1
  • 7
    • 0008285708 scopus 로고    scopus 로고
    • lecture notes, Harvard University
    • R. W. BROCKETT, Stochastic Control, lecture notes, Harvard University, 2009; available online from http://www.eeci-institute.eu/pdf/M015/ RogersStochastic.pdf.
    • (2009) Stochastic Control
    • Brockett, R.W.1
  • 8
    • 0000871390 scopus 로고
    • Lie theory and control systems defined on spheres
    • R. W. BROCKETT, Lie theory and control systems defined on spheres, SIAM J. Appl. Math., 25(1973), pp. 213-225.
    • (1973) SIAM J. Appl. Math. , vol.25 , pp. 213-225
    • Brockett, R.W.1
  • 11
    • 23844446458 scopus 로고    scopus 로고
    • A robust gradient sampling algorithm for nonsmooth, nonconvex optimization
    • J. V. BURKE, A. S. LEWIS, AND M. L. OVERTON, A robust gradient sampling algorithm for nonsmooth, nonconvex optimization, SIAM J. Optim., 15(2005), pp. 751-779.
    • (2005) SIAM J. Optim. , vol.15 , pp. 751-779
    • Burke, J.V.1    Lewis, A.S.2    Overton, M.L.3
  • 12
    • 4344701086 scopus 로고    scopus 로고
    • Comments on "Stochastic stability of jump linear systems"
    • O. COSTA AND M. FRAGOSO, Comments on "Stochastic stability of jump linear systems", IEEE Trans. Automat. Control, 49(2004), pp. 1414-1416.
    • (2004) IEEE Trans. Automat. Control , vol.49 , pp. 1414-1416
    • Costa, O.1    Fragoso, M.2
  • 13
    • 0032625112 scopus 로고    scopus 로고
    • A converse Lyapunov theorem for a class of dynamical systems which undergo switching
    • W. DAYAWANSA AND C. MARTIN, A converse Lyapunov theorem for a class of dynamical systems which undergo switching, IEEE Trans. Automat. Control, 44(1999), pp. 751-760.
    • (1999) IEEE Trans. Automat. Control , vol.44 , pp. 751-760
    • Dayawansa, W.1    Martin, C.2
  • 14
    • 0036646846 scopus 로고    scopus 로고
    • Stochastic stability of jump linear systems
    • Y. FANG AND K. A. LOPARO, Stochastic stability of jump linear systems, IEEE Trans. Automat. Control, 47(2002), pp. 1204-1208.
    • (2002) IEEE Trans. Automat. Control , vol.47 , pp. 1204-1208
    • Fang, Y.1    Loparo, K.A.2
  • 15
    • 77949425195 scopus 로고    scopus 로고
    • Stabilization of Markovian systems via probability rate synthesis and output feedback
    • J.-E. FENG, J. LAM, AND Z. SHU, Stabilization of Markovian systems via probability rate synthesis and output feedback, IEEE Trans. Automat. Control, 55(2010), pp. 773-777.
    • (2010) IEEE Trans. Automat. Control , vol.55 , pp. 773-777
    • Feng, J.-E.1    Lam, J.2    Shu, Z.3
  • 17
    • 77955350346 scopus 로고    scopus 로고
    • Linear copositive Lyapunov functions for continuous-time positive switched systems
    • E. FORNASINI AND M. E. VALCHER, Linear copositive Lyapunov functions for continuous-time positive switched systems, IEEE Trans. Automat. Control, 55(2010), pp. 1933-1937.
    • (2010) IEEE Trans. Automat. Control , vol.55 , pp. 1933-1937
    • Fornasini, E.1    Valcher, M.E.2
  • 18
    • 33746065725 scopus 로고    scopus 로고
    • A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances
    • M. D. FRAGOSO AND O. L. V. COSTA, A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances, SIAM J. Control Optim., 44(2005), pp. 1165-1191.
    • (2005) SIAM J. Control Optim. , vol.44 , pp. 1165-1191
    • Fragoso, M.D.1    Costa, O.L.V.2
  • 19
    • 34447121901 scopus 로고    scopus 로고
    • On the stability of switched positive linear systems
    • L. GURVITS, R. SHORTEN, AND O. MASON, On the stability of switched positive linear systems, IEEE Trans. Automat. Control, 52(2007), pp. 1099-1103.
    • (2007) IEEE Trans. Automat. Control , vol.52 , pp. 1099-1103
    • Gurvits, L.1    Shorten, R.2    Mason, O.3
  • 20
    • 84874263760 scopus 로고    scopus 로고
    • Stability of switched linear systems with Poisson switching
    • B. HANLON, V. TYURYAEV, AND C. MARTIN, Stability of switched linear systems with Poisson switching, Commun. Inf. Syst., 11(2011), pp. 307-326.
    • (2011) Commun. Inf. Syst. , vol.11 , pp. 307-326
    • Hanlon, B.1    Tyuryaev, V.2    Martin, C.3
  • 22
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R. HORN AND C. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1990.
    • (1990) Matrix Analysis
    • Horn, R.1    Johnson, C.2
  • 23
    • 84888317526 scopus 로고    scopus 로고
    • Stochastic stability and robust stabilization of semi-Markov jump linear systems
    • J. HUANG AND Y. SHI, Stochastic stability and robust stabilization of semi-Markov jump linear systems, Internat. J. Robust Nonlinear Control, 23(2013), pp. 2028-2043.
    • (2013) Internat. J. Robust Nonlinear Control , vol.23 , pp. 2028-2043
    • Huang, J.1    Shi, Y.2
  • 24
    • 0038548185 scopus 로고    scopus 로고
    • Coordination of groups of mobile autonomous agents using nearest neighbor rules
    • A. JADBABAIE, J. LIN, AND A. S. MORSE, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48(2003), pp. 988-1001.
    • (2003) IEEE Trans. Automat. Control , vol.48 , pp. 988-1001
    • Jadbabaie, A.1    Lin, J.2    Morse, A.S.3
  • 26
    • 34347331359 scopus 로고    scopus 로고
    • Stability of regime-switching diffusions
    • R. KHASMINSKII, C. ZHU, AND G. YIN, Stability of regime-switching diffusions, Stoch. Process. Appl., 117(2007), pp. 1037-1051.
    • (2007) Stoch. Process. Appl. , vol.117 , pp. 1037-1051
    • Khasminskii, R.1    Zhu, C.2    Yin, G.3
  • 27
    • 67649601053 scopus 로고    scopus 로고
    • On linear co-positive Lyapunov functions for sets of linear positive systems
    • F. KNORN, O. MASON, AND R. SHORTEN, On linear co-positive Lyapunov functions for sets of linear positive systems, Automat., 45(2009), pp. 1943-1947.
    • (2009) Automat. , vol.45 , pp. 1943-1947
    • Knorn, F.1    Mason, O.2    Shorten, R.3
  • 28
    • 0014445822 scopus 로고
    • A survey of stability of stochastic systems
    • F. KOZIN, A survey of stability of stochastic systems, Automatica, 5(1969), pp. 95-112.
    • (1969) Automatica , vol.5 , pp. 95-112
    • Kozin, F.1
  • 29
    • 61349147303 scopus 로고    scopus 로고
    • Stability and stabilizability of switched linear systems: A survey of recent results
    • H. LIN AND P. ANTSAKLIS, Stability and stabilizability of switched linear systems: A survey of recent results, IEEE Trans. Automat. Control, 54(2009), pp. 308-322.
    • (2009) IEEE Trans. Automat. Control , vol.54 , pp. 308-322
    • Lin, H.1    Antsaklis, P.2
  • 30
    • 0003182919 scopus 로고    scopus 로고
    • Stability of stochastic differential equations with Markovian switching
    • X. MAO, Stability of stochastic differential equations with Markovian switching, Stochastic Process. Appl., 79(1999), pp. 45-67.
    • (1999) Stochastic Process. Appl. , vol.79 , pp. 45-67
    • Mao, X.1
  • 31
    • 47249109061 scopus 로고    scopus 로고
    • Stability properties of reset systems
    • D. NEŠIĆ, L. ZACCARIAN, AND A. R. TEEL, Stability properties of reset systems, Automatica, 44(2008), pp. 2019-2026.
    • (2008) Automatica , vol.44 , pp. 2019-2026
    • Nešić, D.1    Zaccarian, L.2    Teel, A.R.3
  • 32
    • 84882928819 scopus 로고    scopus 로고
    • Generalized joint spectral radius and stability of switching systems
    • M. OGURA AND C. MARTIN, Generalized joint spectral radius and stability of switching systems, Linear Algebra Appl., 439(2013), pp. 2222-2239.
    • (2013) Linear Algebra Appl. , vol.439 , pp. 2222-2239
    • Ogura, M.1    Martin, C.2
  • 33
    • 4644244041 scopus 로고    scopus 로고
    • Consensus problems in networks of agents with switching topology and time-delays
    • R. OLFATI-SABER AND R. MURRAY, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49(2004), pp. 1520-1533.
    • (2004) IEEE Trans. Automat. Control , vol.49 , pp. 1520-1533
    • Olfati-Saber, R.1    Murray, R.2
  • 35
    • 84866358966 scopus 로고    scopus 로고
    • Stability of discrete-time switched homogeneous systems on cones and conewise homogeneous inclusions
    • J. SHEN AND J. HU, Stability of discrete-time switched homogeneous systems on cones and conewise homogeneous inclusions, SIAM J. Control Optim., 50(2012), pp. 2216-2253.
    • (2012) SIAM J. Control Optim. , vol.50 , pp. 2216-2253
    • Shen, J.1    Hu, J.2
  • 36
    • 33745617163 scopus 로고    scopus 로고
    • A positive systems model of TCP-like congestion control: Asymptotic results
    • R. SHORTEN, F. WIRTH, AND D. LEITH, A positive systems model of TCP-like congestion control: Asymptotic results, IEEE/ACM Trans. Networking, 14(2006), pp. 616-629.
    • (2006) IEEE/ACM Trans. Networking , vol.14 , pp. 616-629
    • Shorten, R.1    Wirth, F.2    Leith, D.3
  • 37
    • 37249085546 scopus 로고    scopus 로고
    • Stability criteria for switched and hybrid systems
    • R. SHORTEN, F. WIRTH, O. MASON, K. WULFF, AND C. KING, Stability criteria for switched and hybrid systems, SIAM Rev., 49(2007), pp. 545-592.
    • (2007) SIAM Rev. , vol.49 , pp. 545-592
    • Shorten, R.1    Wirth, F.2    Mason, O.3    Wulff, K.4    King, C.5
  • 38
    • 84905021569 scopus 로고    scopus 로고
    • Matrices leaving a cone invariant
    • L. Hogben, ed., Chapter 26, Chapman & Hall/CRC, Boca Raton, FL
    • B.-S. TAM AND H. SCHNEIDER, Matrices leaving a cone invariant, in Handbook of Linear Algebra, L. Hogben, ed., Chapter 26, Chapman & Hall/CRC, Boca Raton, FL, 2006.
    • (2006) Handbook of Linear Algebra
    • Tam, B.-S.1    Schneider, H.2
  • 39
    • 56849094428 scopus 로고    scopus 로고
    • 25 years of HIV-1 research: Progress and perspectives
    • M. A. WAINBERG AND K.-T. JEANG, 25 years of HIV-1 research: Progress and perspectives, BMC Medicine, 6(2008), 31.
    • (2008) BMC Medicine , vol.6 , pp. 31
    • Wainberg, M.A.1    Jeang, K.-T.2
  • 40
    • 84879964535 scopus 로고    scopus 로고
    • On easily verifiable conditions for the existence of common linear copositive Lyapunov functions
    • Z. WU AND Y. SUN, On easily verifiable conditions for the existence of common linear copositive Lyapunov functions, IEEE Trans. Automat. Control, 58(2013), pp. 1862-1865.
    • (2013) IEEE Trans. Automat. Control , vol.58 , pp. 1862-1865
    • Wu, Z.1    Sun, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.