Decoupling in a Class of Nonlinear Systems by State Variable Feedback

1972 ◽  
Vol 94 (4) ◽  
pp. 323-329 ◽  
Author(s):  
S. N. Singh ◽  
W. J. Rugh
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Bilinear Systems ◽  
Decoupling Control ◽  
Control Law ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Laws ◽  
State Variable ◽  
Necessary And Sufficient

For a class of nonlinear systems we derive a necessary and sufficient condition for the existence of a state variable feedback control law which accomplishes decoupling, as well as some conditions which characterize the class of decoupling control laws. Several examples are presented to illustrate the application of these results. For a special subclass which includes the so-called bilinear systems, we give two equivalent forms of the necessary and sufficient condition.

scholarly journals Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Xingao Zhu ◽  
Yuangong Sun
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Nonlinear Systems ◽  
Reachable Set ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Positive Systems ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

Reachable set bounding for homogeneous nonlinear systems with delay and disturbance is studied. By the usage of a new method for stability analysis of positive systems, an explicit necessary and sufficient condition is first derived to guarantee that all the states of positive homogeneous time-delay systems with degree p>1 converge asymptotically within a specific ball. Furthermore, the main result is extended to a class of nonlinear time variant systems. A numerical example is given to demonstrate the effectiveness of the obtained results.

Normal Modal Vibrations for Some Damped n-Degree-of-Freedom Nonlinear Systems

1966 ◽  
Vol 33 (4) ◽  
pp. 877-880 ◽  
Author(s):  
George W. Morgenthaler
Keyword(s):  
Nonlinear Systems ◽  
Normal Mode ◽  
Nonlinear Vibrations ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Damping Matrix ◽  
Necessary And Sufficient ◽  
Do So

T. K. Caughey1 has shown that a necessary and sufficient condition that a damped, linear, n-degree-of-freedom system possess classical linear normal modes is that the damping matrix be diagonalized by the same transformation which uncouples the undamped system. Rosenberg2 has defined normal modes for nonlinear n-degree-of-freedom undamped systems and has shown the existence of such modes for various classes of nonlinear systems. In linear systems, the frequency is independent of the amplitude and, if a set of masses is vibrating in unison, it is not surprising that in some cases they continue to do so as the motion damps out. In nonlinear vibrations, however, frequency depends upon amplitude so that a series of masses vibrating at different amplitudes in a Rosenberg normal mode might generally be expected to lose synchronization as their amplitudes damp out. Two classes of systems are discussed here in which normal modes are preserved under damping, and several examples are given.

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