Robust H2/H∞Control Strategy for Linear Markovian Jump Systems

2014 ◽  
Vol 525 ◽  
pp. 646-652
Author(s):  
Min Bian ◽  
Qing Yun Guo
Keyword(s):  
Control Strategy ◽  
State Feedback ◽  
Control Strategies ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Bounded Real Lemma ◽  
Finite State ◽  
Linear State ◽  
Feasible Solutions ◽  
Jump Systems

The robust H2/<em>H</em>∞ control strategy for a class of linear continuous-time uncertain systems with randomly jumping parameters is investigated. The transition of the jumping parameters is decided by a finite-state Markov process. The uncertainties are supposed to be norm-bounded. It is desired to design a linear state feedback control strategies such that the closed-loop system satisfies H performance and minimizes the H2 norm of the system. A sufficient condition is first established on the existence of the robust H2/<em>H</em>∞controller bases on the bounded real lemma. Then the corresponding state-feedback law is given in terms of a set of linear matrix inequalities (LMIs). It is showed that this condition is equivalent to the feasible solutions problem of LMI. Furthermore, the control strategy design problem is converted into a convex optimization problem subject to LMI constraints, which can be easily solved by standard numerical software.

scholarly journals Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyun Yan ◽  
Yuanhua Qiao ◽  
Lijuan Duan ◽  
Ling Zhang
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Fractional Order ◽  
State Feedback ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Bam Neural Networks ◽  
Linear State ◽  
The Stability

In this paper, the global Mittag–Leffler stabilization of fractional-order BAM neural networks is investigated. First, a new lemma is proposed by using basic inequality to broaden the selection of Lyapunov function. Second, linear state feedback control strategies are designed to induce the stability of fractional-order BAM neural networks. Third, based on constructed Lyapunov function, generalized Gronwall-like inequality, and control strategies, several sufficient conditions for the global Mittag–Leffler stabilization of fractional-order BAM neural networks are established. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

Stabilization and disturbance attenuation control of the gyroscopic inverted pendulum

2020 ◽  
pp. 107754632092914
Author(s):  
Unggul Wasiwitono ◽  
Arif Wahjudi ◽  
Ari K Saputra ◽  
Yohanes
Keyword(s):  
Control Strategy ◽  
State Feedback ◽  
Inverted Pendulum ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Control Moment Gyroscope ◽  
Control Moment ◽  
Unstable Equilibrium Point ◽  
Feedback Control Strategy

In this study, a control moment gyroscope is used as an actuator to stabilize the inverted pendulum. A control strategy is proposed to stabilize the inverted pendulum at the upright unstable equilibrium point and to maintain the gimbal angle as small as possible. Such a problem is formulated as a constrained H∞ disturbance attenuation problem and then transformed into solving linear matrix inequalities. The performance of the proposed controller is evaluated through simulation for linear and nonlinear cases. It is shown that the proposed state-feedback control strategy effectively stabilizes the inverted pendulum.

Robust Absolute Stabilization of Time-Varying Delay Systems with Maximum Admissible Perturbed Bound

2010 ◽  
Vol 40-41 ◽  
pp. 103-110
Author(s):  
Jie Jin
Keyword(s):  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Time Varying ◽  
Time Varying Delay ◽  
Linear State ◽  
Varying Delay ◽  
Nonlinear Delay

This paper is concerned the problem of robust absolute stabilization of time-varying delay systems with admissible perturbation in terms of integral inequality. A linear state-feedback control law is derived for one class of delay systems with sector restriction based on linear matrix inequality (LMI). Especially, this method does not require input terms are absolutely controllable for nonlinear delay systems. Numerical example is used to demonstrate the validity of the proposed method.

Optimal H2 and H∞ Mode-Independent Control for Generalized Bernoulli Jump Systems

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
A. R. Fioravanti ◽  
A. P. C. Gonçalves ◽  
J. C. Geromel
Keyword(s):  
State Feedback ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Random Variable ◽  
Transition Probability Matrix ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Availability Constraints ◽  
Partial Mode ◽  
Jump Systems

This paper deals with state-feedback control of discrete-time linear jump systems. The random variable representing the system modes has a generalized Bernoulli distribution, which is equivalent to a Markov chain where the transition probability matrix has identical rows. Another assumption is about the availability of the mode to the controller. We derive necessary and sufficient linear matrix inequalities (LMI) conditions to design optimal H2 and H∞ state-feedback controllers for the particular class of transition probabilities under consideration and subject to partial mode availability constraints or equivalently cluster availability constraints, which include mode-dependent and mode-independent designs as particular cases. All design conditions are expressed in terms of LMIs. The results are illustrated through a numerical example.

Stochastic Finite-Time Stabilization for Uncertain Jump Systems via State Feedback

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
External Disturbances ◽  
Markov Jump Systems ◽  
Finite State ◽  
Finite Time Stabilization ◽  
Jump Systems

The stochastic finite-time stabilization problem is considered for a class of linear uncertain Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By using the appropriate stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are proposed for the design of stochastic finite-time stabilization controller. The stabilization criteria are formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The designed finite-time stabilized controller makes the stochastic MJSs stochastic finite-time bounded and stochastic finite-time stabilizable for all admissible unknown external disturbances and uncertain parameters. Simulation results illustrate the effectiveness of the developed approaches.

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