scholarly journals Stability of stochastic systems with jumps

1996 ◽  
Vol 3 (2) ◽  
pp. 173-185 ◽  
Author(s):  
E. K. Boukas ◽  
H. Yang
Keyword(s):  
Brownian Motion ◽  
Control Strategy ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
And Brownian Motion ◽  
Quadratic Stabilization ◽  
Guaranteed Cost ◽  
Linear And Nonlinear Systems

This paper deals with stochastic stability of systems with Markovian jumps and Brownian motion. Mainly, we present sufficient conditions for quadratic stabilization of Ito type stochastic linear and nonlinear systems with Markovian jumps and Brownian motion using state feedback control. We also prove the guaranteed cost property of the proposed control strategy for the linear case.

scholarly journals Delay-Dependent Guaranteed Cost Controller Design for Uncertain Neural Networks with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
M. Rajchakit ◽  
P. Niamsup ◽  
T. Rojsiraphisal ◽  
G. Rajchakit
Keyword(s):  
Neural Networks ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Performance Measure ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Guaranteed Cost

This paper studies the problem of guaranteed cost control for a class of uncertain delayed neural networks. The time delay is a continuous function belonging to a given interval but not necessary to be differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, a guaranteed cost controller is designed via memoryless state feedback control, and new sufficient conditions for the existence of the guaranteed cost state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

Mixed H2/H∞ guaranteed cost control for high speed elevator active guide shoe with parametric uncertainties

2020 ◽  
Vol 21 (5) ◽  
pp. 502
Author(s):  
Chen Chen ◽  
Ruijun Zhang ◽  
Qing Zhang ◽  
Lixin Liu
Keyword(s):  
Control Strategy ◽  
High Speed ◽  
State Feedback ◽  
Vibration Suppression ◽  
Ride Comfort ◽  
Optimization Method ◽  
State Feedback Control ◽  
Guide Rail ◽  
Vibration Displacement ◽  
Guaranteed Cost

Aiming at the phenomenon that the elevator car system generates horizontal vibration due to the unevenness of the guide rail and the guide shoe modeling uncertainty caused by friction, wear and spring aging between the rolling guide shoe and the guide rail, a mixed H2/H∞ optimal guaranteed cost state feedback control strategy is proposed. Firstly, as the high-speed elevator car system always exist the phenomenon of stiffness and damping uncertainty in the guide shoe, the LFT method is adopted to construct the state space equation of the car system with parameter uncertainty. Secondly, considering the performance indexes of horizontal acceleration at the center of the car floor and the guide shoe vibration displacement system, an optimal guaranteed performance state feedback controller is designed based on the linear convex optimization method, which to minimize H2 performance index and achieve the specified H∞ performance level. Thirdly, the free matrix is introduced to reduce the conservatism of the controller. Finally, by comparing the simulation results with other control methods under the same conditions, it is verified that the control strategy can make the car system have better vibration suppression ability, and can significantly improve the ride comfort of the elevator.

scholarly journals Optimal Control of Agricultural Insects with a Stage-Structured Model

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Baolin Kang ◽  
Mingfeng He ◽  
Bing Liu
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Control Strategy ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Control Model ◽  
State Feedback Control ◽  
Structured Model ◽  
Feedback Control Strategy ◽  
Order One Periodic Solution

A stage-structured pest control model with impulse effects by state feedback control is formulated, and a semicontinuous dynamic system and its successor functions are defined. The sufficient conditions of existence and attractiveness of order one periodic solution are obtained by the method of successor functions. The superiority of the state feedback control strategy in this paper is that we only need to monitor the sum of immature and mature pest populations. Moreover, our results show that our method used in this paper is more efficient and easier than the existing methods.

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 Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

Sampled-Data State Feedback Stabilization of Boolean Control Networks

2016 ◽  
Vol 28 (4) ◽  
pp. 778-799 ◽  
Author(s):  
Yang Liu ◽  
Jinde Cao ◽  
Liangjie Sun ◽  
Jianquan Lu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Global Stabilization ◽  
Sampled Data ◽  
Control Networks ◽  
Piecewise Constant Control ◽  
Necessary And Sufficient

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

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