scholarly journals New Results on Reachable Set Estimation and Controller Design for Linear Systems with Mixed Delays via Triple Integral Functionals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Kang ◽  
Shouming Zhong
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Controller Design ◽  
Reachable Set ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Closed Loop System ◽  
Set Estimation ◽  
Reachable Set Estimation ◽  
Bounded Disturbance

This paper is concerned with the problem of reachable set estimation and controller design for a class of linear systems with mixed delays and bounded disturbance inputs. By constructing a newly augmented Lyapunov-Krasovskii functional, combining with triple integral technique and reciprocally convex approach, some new reachable set estimation conditions are derived in terms of linear matrix inequalities. Based on these conditions, a state-feedback controller has been designed to ensure the reachable set of the closed-loop system bounded by a given ellipsoid. Finally, two numerical examples are given to illustrate the effectiveness of the proposed analysis and designed method.

scholarly journals Resilient Robust Finite-TimeL2-L∞Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Neutral System ◽  
Time Varying ◽  
Constraint Condition ◽  
Closed Loop System ◽  
Delayed System ◽  
Delay Dependent

The delay-dependent resilient robust finite-timeL2-L∞control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a givenL2-L∞constraint condition. Simulation results illustrate the validity of the proposed approach.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

scholarly journals Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Emerson R. P. da Silva ◽  
Edvaldo Assunção ◽  
Marcelo C. M. Teixeira ◽  
Luiz Francisco S. Buzachero
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Polytopic Uncertainties ◽  
Parameter Dependent ◽  
Finsler’S Lemma ◽  
Time Linear

The motivation for the use of state-derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter-dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state-derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous-time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.

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