The method of rotating lyapunov functions in the stabilization problem for two-dimensional bilinear systems

2000 ◽  
Vol 36 (8) ◽  
pp. 1262-1265 ◽  
Author(s):  
V. V. Fomichev ◽  
A. S. Shepit’ko
Keyword(s):  
Lyapunov Functions ◽  
Bilinear Systems ◽  
Two Dimensional ◽  
Stabilization Problem

scholarly journals Controllability of two-dimensional bilinear systems

1996 ◽  
Vol 15 (2) ◽  
pp. 111-139 ◽  
Author(s):  
Carlos José Braga Barros ◽  
Joao Ribeiro Gonçalves Filho ◽  
Osvaldo Germano Do Rocío ◽  
Luiz A. B. San Martín
Keyword(s):  
Bilinear Systems ◽  
Two Dimensional

H∞ Filtering for two-dimensional discrete switched systems in the second Fornasini and Marchesini model

2020 ◽  
Vol 42 (8) ◽  
pp. 1559-1568
Author(s):  
Khalid Badie ◽  
Mohammed Alfidi ◽  
Zakaria Chalh
Keyword(s):  
Switched Systems ◽  
Lyapunov Functions ◽  
Filter Design ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Reduced Order ◽  
Arbitrary Switching ◽  
Discrete Switched Systems ◽  
Error System ◽  
Filtering Problem

This paper is concerned with the H∞ filtering problem for two-dimensional (2-D) discrete switched systems described by the second Fornasini and Marchesini (FM) model. The main purpose is to design a switched filter such that the resulting filtering error system under the arbitrary switching signal is asymptotically stable with a guaranteed H∞ performance level. By using the switched Lyapunov functions, a new sufficient condition is obtained to guarantee the asymptotic stability with a H∞ performance index for the filtering error system. Based on this condition, the full- and reduced-order H∞ filter design conditions are derived and formulated in terms of linear matrix inequalities (LMIs). Two illustrative examples are utilized to show the effectiveness and less conservativeness of the proposed method.

On the Steady State Motions Control Problem for Mechanical Systems with Relay Controllers

2021 ◽  
Vol 1 (1) ◽  
pp. 48-55
Author(s):  
Aleksandr Andreev ◽  
Olga Peregudova
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Asymptotic Stability ◽  
Control Problem ◽  
Mechanical System ◽  
Lyapunov Functions ◽  
Robot Manipulator ◽  
Mechanical Systems ◽  
Stabilization Problem ◽  
Stability Of The Solution

The paper presents the solution to the stabilization problem of steady state motions for a holonomic mechanical system by using relay controllers. This solution is achieved by proving new theorems on the asymptotic stability of the solution to a differential equation with a discontinuous right-hand side. The novelty of the theorems is based on the limiting inclusions construction and the use of semidefinite Lyapunov functions. As an example, the stabilization problem of steady-state motion for a five-link robot manipulator is solved by using relay controller.

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