Generalized Persistency of Excitation

The paper presents the generalized persistency of excitation conditions. Not only they are valid for much broader range of applications than their classical counterparts but also they elegantly prove the validity of the latter. The novelty and the significance of the approach presented in this publication is due to employing the time averaging technique.

[1]  K. Narendra,et al.  On the uniform asymptotic stability of certain linear nonautonomous differential equations , 1976 .

[2]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[3]  Zvi Artstein,et al.  Uniform asymptotic stability via the limiting equations , 1978 .

[4]  M. Sondhi,et al.  New results on the performance of a well-known class of adaptive filters , 1976, Proceedings of the IEEE.

[5]  G. Kreisselmeier.  Adaptive observers with exponential rate of convergence , 1977 .

[6]  F. J. Narcowich,et al.  Persistency of Excitation in Identification Using Radial Basis Function Approximants , 1995 .

[7]  K. Narendra,et al.  On the Stability of Nonautonomous Differential Equations $\dot x = [A + B(t)]x$, with Skew Symmetric Matrix $B(t)$ , 1977 .

[8]  N. Rouche,et al.  Stability Theory by Liapunov's Direct Method , 1977 .

[9]  Dirk Aeyels,et al.  Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria , 1998, Math. Control. Signals Syst..

[10]  H. Triebel.  Theory Of Function Spaces , 1983 .

[11]  B. Pasik-Duncan,et al.  Adaptive Control , 1996, IEEE Control Systems.

[12]  B. Anderson.  Exponential stability of linear equations arising in adaptive identification , 1977 .

[13]  G. Sansone.  Equazioni differenziali nel campo reale , 1948 .

[14]  K. Narendra,et al.  On the uniform asymptotic stability of certain linear nonautonomous differential equations , 1976 .

[15]  Antonio Loría,et al.  Uniform exponential stability of linear time-varying systems: revisited , 2002, Syst. Control. Lett..

[16]  D. Janecki,et al.  Persistency of excitation for continuous-time systems - Time-domain approach , 1987 .

[17]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[18]  M. A. Jordan,et al.  Persistency of excitation and richness in continuous-time piecewise linear systems , 1997, 1997 1st International Conference, Control of Oscillations and Chaos Proceedings (Cat. No.97TH8329).

[19]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.