Robust stabilization of a class of singularly perturbed discrete bilinear systems

2000 ◽  
Vol 45 (6) ◽  
pp. 1187-1191 ◽  
Author(s):  
Juing-Shian Chiou ◽  
Fan-Chu Kung ◽  
T.-H.S. Li
Keyword(s):  
Robust Stabilization ◽  
Bilinear Systems ◽  
Singularly Perturbed

scholarly journals Robust Stabilization and Observer-Based Stabilization for a Class of Singularly Perturbed Bilinear Systems

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2380
Author(s):  
Ding-Horng Chen ◽  
Chun-Tang Chao ◽  
Juing-Shian Chiou
Keyword(s):  
State Feedback ◽  
Robust Stabilization ◽  
Lyapunov Equation ◽  
Bilinear Systems ◽  
Stability Theorem ◽  
Singularly Perturbed ◽  
Lyapunov Stability Theorem ◽  
Input Gain ◽  
The Stability ◽  
Bounded Input

An infinite-bound stabilization of a system modeled as singularly perturbed bilinear systems is examined. First, we present a Lyapunov equation approach for the stabilization of singularly perturbed bilinear systems for all ε∈(0, ∞). The method is based on the Lyapunov stability theorem. The state feedback constant gain can be determined from the admissible region of the convex polygon. Secondly, we extend this technique to study the observer and observer-based controller of singularly perturbed bilinear systems for all ε∈(0, ∞). Concerning this problem, there are two different methods to design the observer and observer-based controller: one is that the estimator gain can be calculated with known bounded input, the other is that the input gain can be calculated with known observer gain. The main advantage of this approach is that we can preserve the characteristic of the composite controller, i.e., the whole dimensional process can be separated into two subsystems. Moreover, the presented stabilization design ensures the stability for all ε∈(0, ∞). A numeral example is given to compare the new ε-bound with that of previous literature.

Sign in / Sign up

Export Citation Format

Share Document