scholarly journals LMI Formulation for Static Output Feedback Design of Discrete-Time Switched Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Selma Ben Attia ◽  
Salah Salhi ◽  
Mekki Ksouri
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Small Degree ◽  
Switched System ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Additional Degree ◽  
Feedback Design ◽  
And Performance ◽  
Static Output

This paper concerns static output feedback design of discrete-time linear switched system using switched Lyapunov functions (SLFs). A new characterization of stability for the switched system under arbitrary switching is first given together with -performance evaluation. The various conditions are given through a family of LMIs (Linear Matrix Inequalities) parameterized by a scalar variable which offers an additional degree of freedom, enabling, at the expense of a relatively small degree of complexity in the numerical treatment (one line search), to provide better results compared to previous one. The control is defined as a switched static output feedback which guarantees stability and -performance for the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed conditions.

scholarly journals Preview Control for MIMO Discrete-Time System with Parameter Uncertainty

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 756 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
State Feedback ◽  
Mimo Systems ◽  
Multiple Input Multiple Output ◽  
Reference Signal ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Discrete Time System ◽  
Static Output

We consider the problems of state feedback and static output feedback preview controller (PC) for uncertain discrete-time multiple-input multiple output (MIMO) systems based on the parameter-dependent Lyapunov function and the linear matrix inequality (LMI) technique in this paper. First, for each component of a reference signal, an augmented error system (AES) containing previewed information is constructed via the difference operator and state augmentation technique. Then, for the AES, the state feedback and static output feedback are introduced, and when considering the output feedback, a previewable reference signal is utilized by modifying the output equation. The preview controllers’ parameter matrices can be achieved from the solution of LMI problems. The superiority of the PC is illustrated via two numerical examples.

scholarly journals Resilient asynchronous H∞ control designed for discrete-time Markov jump systems: Static output feedback case

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774770
Author(s):  
Xiao Lu ◽  
Lei Yang ◽  
Haixia Wang ◽  
Yuxia Li
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Traffic Control ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Linear Systems ◽  
Static Output

This article is concerned with the problem of resilient asynchronous H∞ static output feedback control for discrete-time Markov jump linear systems. By Finsler’s Lemma, and with the help of two sets of slack variables, the product terms of system matrices and Lyapunov matrices are decoupled. Resilient asynchronous controller is designed to improve the robustness of the controller and overcome the drawback that the controller cannot get the information of the system’s mode. The controller that makes sure the closed-loop system is stochastically stable and with prescribed H∞ performance is designed. The bilinear matrix inequalities are given as the sufficient conditions for the controller design, which can be solved using linear matrix inequalities along with line search. This control strategy can be used in many practical application fields, such as robot control, aircraft, and traffic control.

scholarly journals Robust Stabilization Approach and Performance via Static Output Feedback for a Class of Nonlinear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Neila Bedioui ◽  
Salah Salhi ◽  
Mekki Ksouri
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Robust Stabilization ◽  
Nonlinear Function ◽  
Static Output Feedback ◽  
Additional Degree ◽  
Lmi Optimization ◽  
And Performance ◽  
The Stability ◽  
Static Output

This paper deals with the stability and stabilization problems for a class of discrete-time nonlinear systems. The systems are composed of a linear constant part perturbated by an additive nonlinear function which satisfies a quadratic constraint. A new approach to design a static output feedback controller is proposed. A sufficient condition, formulated as an LMI optimization convex problem, is developed. In fact, the approach is based on a family of LMI parameterized by a scalar, offering an additional degree of freedom. The problem of performance taking into account an criterion is also investigated. Numerical examples are provided to illustrate the effectiveness of the proposed conditions.

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