scholarly journals H_∞ state feedback for linear systems with decentralized control inputs

2020 ◽  
Vol 2 (4) ◽  
pp. 219-231
Author(s):  
Helisyah Nur Fadhilah ◽  
Guisheng Zhai ◽  
Dieky Adzkiya ◽  
Erna Apriliani
Keyword(s):  
Linear Systems ◽  
Directed Graph ◽  
Decentralized Control ◽  
State Feedback ◽  
Design Procedure ◽  
Interconnected Systems ◽  
Matrix Inequality ◽  
Numerical Examples ◽  
Bilinear Matrix Inequality

This paper considers  state feedback with decentralized structure for interconnected systems. The connection between subsystems is described by a directed graph. To design a decentralized  controller, we use the information from its own subsystem and other subsystems based on the interconnection. Decentralized controller is defined as a solution of bilinear matrix inequality (BMI) problem, which is then solved by using the homotopy approach. Two numerical examples are performed to show validity of the design procedure

Controller Gain Design of 2-D Linear Systems Based on the Existing 1-D Analytical Solution

2013 ◽  
Vol 681 ◽  
pp. 55-59
Author(s):  
Wen Jeng Liu
Keyword(s):  
Analytical Solution ◽  
Linear Systems ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Gain ◽  
Two Dimensional ◽  
Numerical Examples ◽  
One Dimensional ◽  
Controller Gain ◽  
Necessary And Sufficient

Abstract. A controller gain design problem of two-dimensional (2-D) linear systems is proposed in this paper. For one-dimensional (1-D) systems, the necessary and sufficient conditions have been established for the problem, and an analytical solution for the feedback gain is given by [1]. Based on the existing 1-D analytical solution, a 2-D state feedback controller gain can be designed to achieve the desired poles. Finally, two numerical examples are shown to exhibit the validity of the proposed approach.

scholarly journals Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 62 (4) ◽  
pp. 889-895 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Reduced Order ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor reduced-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is given and is demonstrated on two numerical examples.

scholarly journals Fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 24 (1) ◽  
pp. 27-37 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is demonstrated on two numerical examples.

New exponential stability criterion for switched linear systems with average dwell time

2018 ◽  
Vol 233 (8) ◽  
pp. 935-944 ◽  
Author(s):  
Yi Gao ◽  
Jiwei Wen ◽  
Li Peng
Keyword(s):  
Exponential Stability ◽  
Stability Criterion ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Computational Procedure ◽  
Matrix Inequality ◽  
Numerical Examples ◽  
Bilinear Matrix Inequality ◽  
Switching Condition ◽  
Stability Issue

In this article, the partition of state space is investigated based on the average dwell time theory, and a novel switching condition is proposed. Under the switching condition and strategy, a switched system where all subsystems are unstable is globally exponentially stabilized. Compared with the existing literature, the conclusion is less conservative and more general. Consequently, the conditions appropriate for this exponential stability issue are derived and a computational procedure to solve the bilinear matrix inequality problems and admissible average dwell time is provided. Finally, two numerical examples are used to show the validity and effectiveness of the proposed methods.

Convex Optimization Approach to Observer-Based Stabilization of Uncertain Linear Systems

2005 ◽  
Vol 128 (4) ◽  
pp. 989-994 ◽  
Author(s):  
Salim Ibrir
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Observer Design ◽  
Linear Matrix ◽  
Computational Algorithms ◽  
Optimization Approach ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
The Stability ◽  
Uncertain Linear Systems

New sufficient linear matrix inequality conditions guaranteeing the stability of uncertain linear systems by means of dynamic output feedbacks are presented. It is shown that the search of an observer-based controller for this class of systems is fundamentally decomposed into two main problems: robust stability with a memoryless state feedback and observer design with measured uncertainties. Under the fulfilment of the developed linear matrix inequalities conditions, we show that the observer-based problem is solvable without any need for some equality constraints or iterative computational algorithms. Examples showing the potential of the results are presented.

Time scale state feedback h-stabilisation of linear systems under Lipschitz-type disturbances

2021 ◽  
pp. 1-11 ◽  
Author(s):  
Bacem Ben Nasser ◽  
Mohamed Djemai ◽  
Michael Defoort ◽  
Taous-Meriem Laleg-Kirati
Keyword(s):  
Linear Systems ◽  
Time Scale ◽  
State Feedback

Dynamic output feedback control for nonlinear large-scale interconnected systems

2020 ◽  
Vol 39 (4) ◽  
pp. 801-821
Author(s):  
Ezzeddine Touti ◽  
Ali Sghaier Tlili ◽  
Muhannad Almutiry
Keyword(s):  
Decentralized Control ◽  
Output Feedback ◽  
Large Scale ◽  
Optimization Problem ◽  
Lyapunov Theory ◽  
Interconnected Systems ◽  
Dynamic Output Feedback ◽  
Content Type ◽  
Dynamic Output ◽  
Control Scheme

Purpose This paper aims to focus on the design of a decentralized observation and control method for a class of large-scale systems characterized by nonlinear interconnected functions that are assumed to be uncertain but quadratically bounded. Design/methodology/approach Sufficient conditions, under which the designed control scheme can achieve the asymptotic stabilization of the augmented system, are developed within the Lyapunov theory in the framework of linear matrix inequalities (LMIs). Findings The derived LMIs are formulated under the form of an optimization problem whose resolution allows the concurrent computation of the decentralized control and observation gains and the maximization of the nonlinearity coverage tolerated by the system without becoming unstable. The reliable performances of the designed control scheme, compared to a distinguished decentralized guaranteed cost control strategy issued from the literature, are demonstrated by numerical simulations on an extensive application of a three-generator infinite bus power system. Originality/value The developed optimization problem subject to LMI constraints is efficiently solved by a one-step procedure to analyze the asymptotic stability and to synthesize all the control and observation parameters. Therefore, such a procedure enables to cope with the conservatism and suboptimal solutions procreated by optimization problems based on iterative algorithms with multi-step procedures usually used in the problem of dynamic output feedback decentralized control of nonlinear interconnected systems.

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