TY - GEN

T1 - Lyapunov functions for uncertain systems with applications to the stability of time varying systems

AU - Chockalingam, Ganapathy

AU - Dasgupta, Soura

AU - Anderson, Brian D.O.

AU - Fu, Minyue

PY - 1993

Y1 - 1993

N2 - This paper has three contributions. The first involves polytopes of matrices whose characteristic polynomials also lie in a polytopic set (e.g. companion matrices). We show that this set is Hurwitz or Schur invariant if there exist multiaffinely parameterized positive definite, Lyapunov matrices which solve an augmented Lyapunov equation. The second result concerns uncertain transfer functions with denominator and numerator belonging to a polytopic set. We show all members of this set are Strictly Positive Real iff the Lyapunov matrices solving the equations featuring the Kalman-Yakubovic-Popov Lemma are multiaffinely parameterized. Moreover, under an alternative characterization of the underlying polytopic sets, the Lyapunov matrices for both of these results admit affine parameterizations. Finally, we apply the Lyapunov equation results to derive stability conditions for a class of Linear Time Varying Systems.

AB - This paper has three contributions. The first involves polytopes of matrices whose characteristic polynomials also lie in a polytopic set (e.g. companion matrices). We show that this set is Hurwitz or Schur invariant if there exist multiaffinely parameterized positive definite, Lyapunov matrices which solve an augmented Lyapunov equation. The second result concerns uncertain transfer functions with denominator and numerator belonging to a polytopic set. We show all members of this set are Strictly Positive Real iff the Lyapunov matrices solving the equations featuring the Kalman-Yakubovic-Popov Lemma are multiaffinely parameterized. Moreover, under an alternative characterization of the underlying polytopic sets, the Lyapunov matrices for both of these results admit affine parameterizations. Finally, we apply the Lyapunov equation results to derive stability conditions for a class of Linear Time Varying Systems.

UR - http://www.scopus.com/inward/record.url?scp=0027875127&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027875127

SN - 0780312988

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1525

EP - 1530

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

T2 - Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4)

Y2 - 15 December 1993 through 17 December 1993

ER -