Parameter-dependent Lyapunov functions and the discrete-time Popov criterion for robust analysis

✍ Scribed by Wassim M. Haddad; Dennis S. Bernstein

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 576 KB
• Volume: 30
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(94)90195-3

✦ Synopsis

Almhmct--Parameterodependent Lyapunov functions are developed for discrete-time systems with constant real parameter uncertainty. This construction of a family of Lyapanov functions is then used to analyze robust stability with He performance bounds for state space systems. A special case of these results generalizes the classical discrete-time Popov criterion.

Notation

R, R "×', R"

C, C r×', C r E, tr, Orxs 1,, ()T,(), p(), o,,.,,, 5", N', P" ZI < Z2, Zt < Z2 Ilxlh IIZlIF IIH(z)lh real numbers, r x s real matrices, R "x~ complex numbers, r xs complex matrices, C rx I expectation, trace, r x s zero matrix r x r identity, transpose, complex conjugate transpose spectral radius, largest singular value r x r symmetric, negative-definite, positive-definite matrices Z 2 -Z I ¢ N r, Z 2 -ZI E pr Zl ' Z2 E 5 r Ix*x] '~, x e C r [tr ZZ*] ta (Frobenius matrix norm) [(1/2~)f~_,, IIH(e~°)ll 2 dO] trz *