Computing regions of attraction with polytopes: Planar case

Automatica

Volumn 32, Issue 12, 1996, Pages 1727-1732

  Romanchuk, B G ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Lyapunov stability; Numerical algorithms; Piecewise linear analysis; Saturation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ESTIMATION; FEEDBACK; FUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PIECEWISE LINEAR TECHNIQUES; SET THEORY;

LYAPUNOV FUNCTION; NONLINEAR TRANSFORMATION; POLYTOPES;

CONTROL THEORY;

EID: 0030387765     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(96)80011-2     Document Type: Article

References (11)

1. Bitsons, G. and M. Vassilaki (1995). Constrained regulation of linear systems. Automatica, 31, 223-227.
2. Brøndsted, A. (1983). An Introduction to Convex Polytopes. Springer-Verlag, New York.
3. Chvátal, V. (1983). Linear Programming. Freeman, New York.
4. Fleming, W. and H. Soner (1993). Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York.
5. Gutman, P.-O. and M. Cwikel (1987). An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states. IEEE Trans. Autom. Control, AC-32, 251-254.
6. James, M. (1993). A partial differential inequality for dissipative nonlinear systems. Syst. Control Lett., 21, 315-320.
7. Romanchuk, B. (1996). A polytope based algorithm to compute regions of attraction. Technical Report TR-CIM-96-04, McGill Centre For Intelligent Machines, Montreal.
8. Sontag, E. (1981). Nonlinear regulation: the piecewise linear approach. IEEE Trans. Autom. Control, AC-26, 346-357.
9. Sontag, E. (1990). Mathematical Control Theory. Springer-Verlag, New York.
10. Tarboureich, S. and C. Burgat (1994). Positively invariant sets for constrained continuous-time systems with cone properties. IEEE Trans. Autom. Control, AC-39, 401-405.
11. Vassilaki, M. and G. Bitsoris (1989). Constrained regulation of linear continuous-time dynamical systems. Syst. Control Lett., 13, 247-252.