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A numerical sufficiency test for the asymptotic stability of linear time-varying Hurwitz systems is proposed. The algorithmic procedure constructs a bounding tube in which the state is guaranteed to stay. The continuous-time system is evaluated at discrete time instants, for which successive quadratic Lyapunov functions are generated. The tube is constructed based on: (i) a conservative estimate of the state evolution, from a discrete time instant to the next, obtained from the corresponding Lyapunov function, and (ii) re-evaluation of the tube diameter at each discrete time instant to account for variations in the plant matrix. The numerical test is illustrated in simulation via both a stable and an unstable system.

[1]  Francesco Amato,et al.  New sufficient conditions for the stability of slowly varying linear systems , 1993, IEEE Trans. Autom. Control..

[2]  K. S. P. Kumar,et al.  An alternate stability analysis framework for adaptive control N , 1986 .

[3]  Baxter F. Womack,et al.  Comments on "On the Lyapunov matrix equation" , 1975 .

[4]  Charles A. Desoer,et al.  Slowly varying system ẋ = A(t)x , 1969 .

[5]  Pravin Varaiya,et al.  On Ellipsoidal Techniques for Reachability Analysis. Part II: Internal Approximations Box-valued Constraints , 2002, Optim. Methods Softw..

[6]  D. Owens,et al.  Sufficient conditions for stability of linear time-varying systems , 1987 .

[7]  H. H. Rosenbrook.  The Stability of Linear Time-dependent Control Systems† , 1963 .

[8]  Wilson J. Rugh,et al.  Analytical Framework for Gain Scheduling , 1990, 1990 American Control Conference.

[9]  M. A. Krasnoselʹskii.  Topological methods in the theory of nonlinear integral equations , 1968 .

[10]  Wilson J. Rugh,et al.  A stability result for linear parameter-varying systems , 1995 .

[11]  Roy M. Howard,et al.  Linear System Theory , 1992 .

[12]  André I. Khuri,et al.  Infinite Sequences and Series , 2003 .

[13]  S. Bialas.  On the Lyapunov matrix equation , 1980 .

[14]  Gerhard Kreisselmeier,et al.  An approach to stable indirect adaptive control , 1985, Autom..

[15]  Pravin Varaiya,et al.  Ellipsoidal Techniques for Reachability Analysis , 2000, HSCC.

[16]  A. Fuller,et al.  Stability of Motion , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Pravin Varaiya,et al.  On Ellipsoidal Techniques for Reachability Analysis. Part I: External Approximations , 2002, Optim. Methods Softw..