scholarly journals Feedback stabilization of discrete-time nonlinear systems via the control Lyapunov functions

2003 ◽  
Author(s):  
A. Iggidr ◽  
M. Oumoun ◽  
J.C. Vivalda
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Feedback Stabilization

scholarly journals Interval criterion for stability analysis of discrete-time nonlinear systems with partial state saturation nonlinearities

2006 ◽  
Vol 19 (2) ◽  
pp. 271-286
Author(s):  
Lubomir Kolev ◽  
Simona Filipova-Petrakieva ◽  
Valeri Mladenov
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Interval Uncertainties ◽  
Partial State ◽  
Definite Interval ◽  
Outer Bounds ◽  
State Saturation

A generalization of sufficient conditions for global asymptotic stability of the equilibrium of discrete-time nonlinear systems with saturation non linearity's on part of the states in the case of interval uncertainties is considered. When using quadratic form Lyapunov functions, sufficient conditions based on the positive definite interval matrices are presented. In order to check this, a recently proposed method for determining the outer bounds of eigenvalues ranges is used. A numerical example illustrating the applicability of the method suggested is solved in the end of the paper.

scholarly journals Robust State Feedback Stabilization of Uncertain Discrete-Time Switched Linear Systems Subject to Actuator Saturation

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xinquan Zhang ◽  
Guoliang Wang ◽  
Jun Zhao
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Domain Of Attraction ◽  
Feedback Stabilization ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Lyapunov Functions Method

The robust stabilization problem is investigated for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the multiple Lyapunov functions method. A switching law and a state feedback law are designed to asymptotically stabilize the system with a large domain of attraction. Based on the multiple Lyapunov functions method, sufficient conditions are obtained for robust stabilization. Furthermore, when some parameters are given in advance, the state feedback controllers and the estimation of domain of attraction are presented by solving a convex optimization problem subject to a set of linear matrix inequalities (LMI) constraints. A numerical example is given to show the effectiveness of the proposed technique.

scholarly journals Control of discrete-time nonlinear systems via finite-step control Lyapunov functions

2020 ◽  
Vol 138 ◽  
pp. 104631
Author(s):  
Navid Noroozi ◽  
Roman Geiselhart ◽  
Lars Grüne ◽  
Fabian R. Wirth
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Finite Step ◽  
Step Control
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