A new linear matrix inequality condition for robust D-stabilizing proportional-derivative state-feedback controller design of polynomial matrix polytopes

ICCAS 2010 ◽  
2010 ◽  
Author(s):  
Dong-Hwan Lee ◽  
Jin-Bae Park ◽  
Young-Hoon Joo
Keyword(s):  
Linear Matrix Inequality ◽  
State Feedback ◽  
Controller Design ◽  
Polynomial Matrix ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
State Feedback Controller

scholarly journals Output Strictly Passive Control of Uncertain Singular Neutral Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Jichun Wang ◽  
Qingling Zhang ◽  
Dong Xiao
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
State Feedback ◽  
Passive Control ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Neutral Systems ◽  
Previous Approach ◽  
State Feedback Controller

This paper concerns the problem of output strictly passive control for uncertain singular neutral systems. It introduces a new effective criterion to study the passivity of singular neutral systems. Compared with the previous approach, this criterion has no equality constraints. And the state feedback controller is designed so that the uncertain singular neutral systems are output strictly passive. In terms of a linear matrix inequality (LMI) and Lyapunov function, the strictly passive criterion is formulated. And the desired passive controller is given. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.

scholarly journals Quantized State-Feedback Stabilization for Delayed Markovian Jump Linear Systems with Generally Incomplete Transition Rates

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanbo Li ◽  
Peng Zhang ◽  
Yonggui Kao ◽  
Hamid Reza Karimi
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Transition Rates ◽  
Markovian Jump ◽  
Input Quantization ◽  
State Feedback Controller ◽  
Markovian Jump Linear Systems

This paper is concerned with the robust quantized state-feedback controller design problem for a class of continuous-time Markovian jump linear uncertain systems with general uncertain transition rates and input quantization. The uncertainties under consideration emerge in both system parameters and mode transition rates. This new uncertain model is more general than the existing ones and can be applicable to more practical situations because each transition rate can be completely unknown or only its estimate value is known. Based on linear matrix inequalities, the quantized state-feedback controller is formulated to ensure the closed-loop system is stable in mean square. Finally, a numerical example is presented to verify the validity of the developed theoretical results.

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

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