scholarly journals H∞Enhanced Control Design of Discrete-Time Takagi-Sugeno State-Multiplicative Noisy Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
State Feedback Control ◽  
Control Law ◽  
State Control ◽  
Bounded Real Lemma ◽  
Quadratic Performance ◽  
The Mean ◽  
Takagi Sugeno

Design conditions for existence of theH∞state feedback control for Takagi-Sugeno fuzzy discrete-time stochastic systems with state-multiplicative noise, stabilizing the closed-loop in such way that the quadratic performance in the mean is satisfied, are presented in the paper. Using newly introduced enhanced form of the bounded real lemma for such stochastic systems, the LMI-based procedure is provided for computation of gain matrices of the state control law, realized in the parallel distributed compensation structure. The approach is illustrated on an example, demonstrating the validity of the proposed method.

scholarly journals H∞ control of discrete-time linear systems constrained in state by equality constraints

2012 ◽  
Vol 22 (3) ◽  
pp. 551-560 ◽  
Author(s):  
Anna Filasová ◽  
Dušan Krokavec
Keyword(s):  
Discrete Time ◽  
Design Procedure ◽  
Equality Constraints ◽  
State Feedback Control ◽  
Computation Method ◽  
Control Law ◽  
State Variables ◽  
Bounded Real Lemma ◽  
Time Systems ◽  
Time Linear

Abstract In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outperforms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.

scholarly journals Robust Stability, Stabilization, andH∞Control of a Class of Nonlinear Discrete Time Stochastic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Tianliang Zhang ◽  
Yu-Hong Wang ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
State Control ◽  
Stochastic Stabilizability ◽  
Discrete Stochastic System

This paper studies robust stability, stabilization, andH∞control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robustH∞state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robustH∞performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.

scholarly journals State Feedback Guaranteed Cost Repetitive Control for Uncertain Discrete-Time Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Wentao Chen ◽  
Yechun Lin ◽  
Qingping Wu
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Cost Control ◽  
Repetitive Control ◽  
Guaranteed Cost Control ◽  
State Feedback Control ◽  
Control Law ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method so that the closed-loop repetitive control system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. The state feedback control technique is used in the paper. While for the case that the states are not measurable, an observer-based control scheme is adopted. Sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI). The control and observer gains are characterized by the feasible solutions to these LMIs. The optimal guaranteed cost control law is obtained efficiently by solving an optimization problem with LMI constraints using existing convex optimization algorithms. A simulation example is provided to illustrate the validity of the proposed method.

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.

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