Nonlinear Input-output Stability and Stabilization

1997 ◽  
pp. 373-388
Author(s):  
A. R. Teel
Keyword(s):  
Input Output ◽  
Output Stability ◽  
Nonlinear Input ◽  
Stability And Stabilization

Stability Criteria for Distributed Nonlinear Sampled-Data Systems Defined by Green’s Functions

1974 ◽  
Vol 96 (3) ◽  
pp. 315-321 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Stability Criterion ◽  
Feedback Gain ◽  
Continuous Systems ◽  
Mean Square ◽  
Data Systems ◽  
Sampled Data ◽  
Input Output ◽  
Output Stability ◽  
Lumped Parameter ◽  
The Mean

Sampled-data, nonlinear, distributed systems, which exhibit a structure similar to that of the standard closed loop with lumped parameter, are investigated from the viewpoint of their input-output stability. These systems are governed by operational equations involving discrete Laplace-Green kernels. Their feedback gains are bounded by upper and lower values which depend explicitly on the time and the distributed parameter. The main result is: an input-output stability theorem is given which applies both in L∞ (O, ∞) and L2 (O, ∞). This criterion, which may be considered as being an extension of the ≪circle criterion≫, involves the mean square value on the bounds of the feedback gain. Stability conditions for continuous systems are derived from this result. In the special case of systems with distributed periodical time-varying feedback gains, a stability criterion is given which applies in Marcinkiewicz space M2 (O, ∞). This result which involves the mean square value of the feedback gain is generally less restrictive than the L2 (O, ∞) stability criterion mentioned above.

A Nonlinear Input-Output Model of a Multisectored Economy

Econometrica ◽  
1973 ◽  
Vol 41 (6) ◽  
pp. 1167 ◽  
Author(s):  
I. W. Sandberg
Keyword(s):  
Input Output ◽  
Nonlinear Input

scholarly journals Input–output finite-region stability and stabilization for discrete 2-D Fornasini–Marchesini models

2017 ◽  
Vol 99 ◽  
pp. 9-16 ◽  
Author(s):  
Guangchen Zhang ◽  
Harry L. Trentelman ◽  
Weiqun Wang ◽  
Jingbo Gao
Keyword(s):  
Finite Region ◽  
Input Output ◽  
Stability And Stabilization
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