메뉴 건너뛰기




Volumn , Issue , 2010, Pages 131-139

On infinity norms as Lyapunov functions for piecewise affine systems

Author keywords

Infinity norms; Lyapunov methods; Output feedback; Piecewise affine systems; Stability

Indexed keywords

BILINEAR MATRIX INEQUALITY; DISCRETE-TIME; INFINITY NORM; INFINITY NORMS; LINEAR PROGRAMS; NEW SOLUTIONS; OUTPUT FEEDBACK; OUTPUT FEEDBACK CONTROLS; PIECE-WISE; PIECEWISE AFFINE SYSTEMS; QUADRATIC LYAPUNOV FUNCTION; S-PROCEDURES; STABILIZING STATE; STATIC FEEDBACK CONTROL;

EID: 77953039358     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1755952.1755972     Document Type: Conference Paper
Times cited : (18)

References (29)
  • 1
    • 0031701911 scopus 로고    scopus 로고
    • A unified framework for hybrid control: Model and optimal control theory
    • M. S. Branicky, V. S. Borkar, and S. K. Mitter, "A unified framework for hybrid control: model and optimal control theory," IEEE Transactions on Automatic Control, vol. 43, no. 1, pp. 31-45, 1998.
    • (1998) IEEE Transactions on Automatic Control , vol.43 , Issue.1 , pp. 31-45
    • Branicky, M.S.1    Borkar, V.S.2    Mitter, S.K.3
  • 2
    • 0003674491 scopus 로고    scopus 로고
    • Ph.D. dissertation, Lund Institute of Technology, Sweden
    • M. Johansson, "Piecewise linear control systems," Ph.D. dissertation, Lund Institute of Technology, Sweden, 1999.
    • (1999) Piecewise Linear Control Systems
    • Johansson, M.1
  • 4
    • 0019559589 scopus 로고
    • Nonlinear regulation: The piecewise linear approach
    • E. D. Sontag, "Nonlinear regulation: the piecewise linear approach," IEEE Transactions on Automatic Control, vol. 26, no. 2, pp. 346-357, 1981.
    • (1981) IEEE Transactions on Automatic Control , vol.26 , Issue.2 , pp. 346-357
    • Sontag, E.D.1
  • 5
    • 0032045898 scopus 로고    scopus 로고
    • Computation of piecewise quadratic Lyapunov functions for hybrid systems
    • M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 555-559, 1998.
    • (1998) IEEE Transactions on Automatic Control , vol.43 , Issue.4 , pp. 555-559
    • Johansson, M.1    Rantzer, A.2
  • 6
    • 0036888056 scopus 로고    scopus 로고
    • Analysis of discrete-time piecewise affine and hybrid systems
    • G. Ferrari-Trecate, F. A. Cuzzola, D. Mignone, and M. Morari, "Analysis of discrete-time piecewise affine and hybrid systems," Automatica, vol. 38, no. 12, pp. 2139-2146, 2002.
    • (2002) Automatica , vol.38 , Issue.12 , pp. 2139-2146
    • Ferrari-Trecate, G.1    Cuzzola, F.A.2    Mignone, D.3    Morari, M.4
  • 7
    • 0036857323 scopus 로고    scopus 로고
    • Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach
    • J. Daafouz, P. Riedinger, and C. Iung, "Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach," IEEE Transactions on Automatic Control, vol. 47, pp. 1883-1887, 2002.
    • (2002) IEEE Transactions on Automatic Control , vol.47 , pp. 1883-1887
    • Daafouz, J.1    Riedinger, P.2    Iung, C.3
  • 10
    • 45249096257 scopus 로고    scopus 로고
    • Global input-to-state stability and stabilization of discrete-time piece-wise affine systems
    • M. Lazar and W. P. M. H. Heemels, "Global input-to-state stability and stabilization of discrete-time piece-wise affine systems," Nonlinear Analysis: Hybrid Systems, vol. 2, pp. 721-734, 2008.
    • (2008) Nonlinear Analysis: Hybrid Systems , vol.2 , pp. 721-734
    • Lazar, M.1    Heemels, W.P.M.H.2
  • 13
    • 70350026658 scopus 로고    scopus 로고
    • Observer-based control of linear complementarity systems
    • Hybrid Systems: Computation and Control, ser. Springer-Verlag
    • W. P. M. H. Heemels, M. K. Camlibel, B. Brogliato, and J. M. Schumacher, "Observer-based control of linear complementarity systems," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, vol. 4981. Springer-Verlag, 2008, pp. 259-272.
    • (2008) Lecture Notes in Computer Science , vol.4981 , pp. 259-272
    • Heemels, W.P.M.H.1    Camlibel, M.K.2    Brogliato, B.3    Schumacher, J.M.4
  • 14
    • 0024702510 scopus 로고
    • Criteria of asymptotic stability of differential and difference inclusions encountered in control theory
    • A. P. Molchanov and E. S. Pyatnitskii, "Criteria of asymptotic stability of differential and difference inclusions encountered in control theory," Systems & Control Letters, vol. 13, pp. 59-64, 1989.
    • (1989) Systems & Control Letters , vol.13 , pp. 59-64
    • Molchanov, A.P.1    Pyatnitskii, E.S.2
  • 15
  • 16
    • 0029344521 scopus 로고
    • On infinity norms as Lyapunov functions for linear systems
    • A. Polański, "On infinity norms as Lyapunov functions for linear systems," IEEE Transactions on Automatic Control, vol. 40, no. 7, pp. 1270-1273, 1995.
    • (1995) IEEE Transactions on Automatic Control , vol.40 , Issue.7 , pp. 1270-1273
    • Polański, A.1
  • 17
    • 0031190320 scopus 로고    scopus 로고
    • Lyapunov function construction by linear programming
    • -, "Lyapunov function construction by linear programming," IEEE Transactions on Automatic Control, vol. 42, no. 7, pp. 1013-1016, 1997.
    • (1997) IEEE Transactions on Automatic Control , vol.42 , Issue.7 , pp. 1013-1016
  • 18
    • 0010969679 scopus 로고    scopus 로고
    • Further comments on "Vector norms as Lyapunov functions for linear systems"
    • K. Loskot, A. Polański, and R. Rudnicki, "Further comments on "Vector norms as Lyapunov functions for linear systems"," IEEE Transactions on Automatic Control, vol. 43, no. 2, pp. 289-291, 1998.
    • (1998) IEEE Transactions on Automatic Control , vol.43 , Issue.2 , pp. 289-291
    • Loskot, K.1    Polański, A.2    Rudnicki, R.3
  • 19
    • 0343517454 scopus 로고    scopus 로고
    • On absolute stability analysis by polyhedral Lyapunov functions
    • A. Polański, "On absolute stability analysis by polyhedral Lyapunov functions," Automatica, vol. 36, pp. 573-578, 2000.
    • (2000) Automatica , vol.36 , pp. 573-578
    • Polański, A.1
  • 20
    • 0032632143 scopus 로고    scopus 로고
    • A parametrization of piecewise linear Lyapunov functions via linear programming
    • P. Julián, J. Guivant, and A. Desages, "A parametrization of piecewise linear Lyapunov functions via linear programming," International Journal of Control, vol. 72, no. 7/8, pp. 702-715, 1999.
    • (1999) International Journal of Control , vol.72 , Issue.7-8 , pp. 702-715
    • Julián, P.1    Guivant, J.2    Desages, A.3
  • 21
    • 85008047666 scopus 로고    scopus 로고
    • Further results on "Infinity norms as Lyapunov functions for linear systems"
    • F. J. Christophersen and M. Morari, "Further results on "Infinity norms as Lyapunov functions for linear systems"," IEEE Transactions on Automatic Control, vol. 52, no. 3, pp. 547-553, 2007.
    • (2007) IEEE Transactions on Automatic Control , vol.52 , Issue.3 , pp. 547-553
    • Christophersen, F.J.1    Morari, M.2
  • 22
    • 0029266878 scopus 로고
    • Nonquadratic Lyapunov functions for robust control
    • F. Blanchini, "Nonquadratic Lyapunov functions for robust control," Automatica, vol. 31, no. 3, pp. 451-461, 1995.
    • (1995) Automatica , vol.31 , Issue.3 , pp. 451-461
    • Blanchini, F.1
  • 23
    • 34247276984 scopus 로고    scopus 로고
    • Switching stabilizability for continuous-time uncertain switched linear systems
    • H. Lin and P. J. Antsaklis, "Switching stabilizability for continuous-time uncertain switched linear systems," IEEE Transactions on Automatic Control, vol. 52, no. 4, pp. 633-646, 2007.
    • (2007) IEEE Transactions on Automatic Control , vol.52 , Issue.4 , pp. 633-646
    • Lin, H.1    Antsaklis, P.J.2
  • 24
    • 24344500258 scopus 로고    scopus 로고
    • Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems
    • Hybrid Systems: Computation and Control, ser. Zürich, Switzerland: Springer Verlag
    • M. Lazar, W. P. M. H. Heemels, S. Weiland, A. Bemporad, and O. Pastravanu, "Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, vol. 3414. Zürich, Switzerland: Springer Verlag, 2005, pp. 417-432.
    • (2005) Lecture Notes in Computer Science , vol.3414 , pp. 417-432
    • Lazar, M.1    Heemels, W.P.M.H.2    Weiland, S.3    Bemporad, A.4    Pastravanu, O.5
  • 26
    • 67650112943 scopus 로고    scopus 로고
    • Synthesis of trajectory-dependent control Lyapunov functions by a single linear program
    • Hybrid Systems: Computation and Control, ser. Springer-Verlag
    • M. Lazar and A. Jokic, "Synthesis of trajectory-dependent control Lyapunov functions by a single linear program," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, vol. 5469. Springer-Verlag, 2009, pp. 237-251.
    • (2009) Lecture Notes in Computer Science , vol.5469 , pp. 237-251
    • Lazar, M.1    Jokic, A.2
  • 27
    • 0037079760 scopus 로고    scopus 로고
    • A converse Lyapunov theorem for discrete-time systems with disturbances
    • Z.-P. Jiang and Y. Wang, "A converse Lyapunov theorem for discrete-time systems with disturbances," Systems & Control Letters, vol. 45, pp. 49-58, 2002.
    • (2002) Systems & Control Letters , vol.45 , pp. 49-58
    • Jiang, Z.-P.1    Wang, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.