Robust stabilization for continuous-time systems with slowly time-varying uncertain real parameters

The authors construct a class of parameter-dependent Lyapunov functions to guarantee robust stability in the presence of time-varying rate restricted plant uncertainty. Extensions to a class of time-varying nonlinear uncertainty that generalize the multivariable Popov criterion are also considered. These results are then used for controller synthesis to address the problem of robust stabilization in the presence of slowly time-varying real parameters.

[1]  B. Friedland.  On the properties of reduced-order Kalman filters , 1987, 26th IEEE Conference on Decision and Control.

[2]  Stability criteria for non-stationary feedback systems† , 1968 .

[3]  S. Bittanti,et al.  Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty , 1996 .

[4]  Fu-Chuang Chen,et al.  Optimal solution of the two-stage Kalman estimator , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[5]  J. M. Mendel,et al.  Multistage Estimation of Bias States in Linear Systems. , 1978 .

[6]  Finite regions of attraction for feedback systems containing a single time-varying nonlinearity , 1968 .

[7]  Liapunov Functions for Feedback Systems Containing a Single Time-varying Non-linearity† , 1968 .

[8]  Brian D. O. Anderson,et al.  Algebraic Structure of Generalized Positive Real Matrices , 1968 .

[9]  A. Bryson,et al.  Linear filtering for time-varying systems using measurements containing colored noise , 1965 .

[10]  D. Bernstein,et al.  Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis , 1995, IEEE Trans. Autom. Control..

[11]  M. Ignagni,et al.  Separate bias Kalman estimator with bias state noise , 1990 .

[12]  T. R. Rice,et al.  On the optimality of two-stage state estimation in the presence of random bias , 1993, IEEE Trans. Autom. Control..

[13]  Dennis S. Bernstein,et al.  Generalized mixed-μ bounds for real and complex multiple-block uncertainty with internal matrix structure , 1995 .

[14]  Z. Rekasius,et al.  A stability criterion for feedback systems containing a single time-varying nonlinear element , 1965 .

[15]  M. Gruber,et al.  On a generalization of the circle criterion. , 1966 .

[16]  B. Friedland.  Treatment of bias in recursive filtering , 1969 .

[17]  M. Ignagni.  An alternate derivation and extension of Friendland's two-stage Kalman estimator , 1981 .

[18]  M. Thathachar,et al.  Stability of a Class of Non-linear Time-varying Systems† , 1968 .