Control System Analysis and Design Via the “Second Method” of Lyapunov: II—Discrete-Time Systems

1960 ◽  
Vol 82 (2) ◽  
pp. 394-400 ◽  
Author(s):  
R. E. Kalman ◽  
J. E. Bertram
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
System Analysis ◽  
Companion Paper ◽  
Data Systems ◽  
Sampled Data ◽  
Analysis And Design ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Second Method Of Lyapunov

The second method of Lyapunov is applied to the study of discrete-time (sampled-data) systems. With minor variations, the discussion parallels that of the companion paper on continuous-time systems. Theorems are stated in full but motivation, proofs, examples, and so on, are given only when they differ materially from their counterparts in the continuous-time case.

Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems

1960 ◽  
Vol 82 (2) ◽  
pp. 371-393 ◽  
Author(s):  
R. E. Kalman ◽  
J. E. Bertram
Keyword(s):  
Control System ◽  
System Analysis ◽  
Transient Behavior ◽  
System Optimization ◽  
Companion Paper ◽  
Analysis And Design ◽  
Continuous Time Systems ◽  
The Subject ◽  
Time Systems ◽  
Second Method Of Lyapunov

The “second method” of Lyapunov is the most general approach currently in the theory of stability of dynamic systems. After a rigorous exposition of the fundamental concepts of this theory, applications are made to (a) stability of linear stationary, linear nonstationary, and nonlinear systems; (b)estimation of transient behavior; (c) control-system optimization; (d) design of relay servos. The discussion is essentially self-contained, with emphasis on the thorough development of the principal ideas and mathematical tools. Only systems governed by differential equations are treated here. Systems governed by difference equations are the subject of a companion paper.

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