| 摘要: |
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| DOI： |
| Received:April 08, 2014Revised:July 04, 2014 |
| 基金项目: |
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| On the ${\ell}_2$-stability of time-varying linear and nonlinear discrete-time MIMO systems |
| Y. V. Venkatesh |
| (Department of ECE, National University of Singapore; Electrical Sciences, Indian Institute of Science) |
| Abstract: |
| New conditions are derived for the ?2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput
(MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a
matrix of periodic/aperiodic gains A(k), k = 0, 1, 2, . . . and a vector of certain classes of non-monotone/monotone nonlinearities
φ_(·_), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions,
which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real
part (as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of
multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which
allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of
(A(k + 1),A(k)), k = 1, 2, . . . . iii) They are distinct from and less restrictive than recent results in the literature. |
| Key words: Circle criterion Discrete-time MIMO system 2-stability Feedback system stability Linear matrix inequalities(LMI) Lur’e problem Multiplier functions Nyquist’s criterion Periodic coefficient systems Popov’s criterion Time-varyingsystems |
