scholarly journals Delay-Dependent Finite-TimeH∞Controller Design for a Kind of Nonlinear Descriptor Systems via a T-S Fuzzy Model

2015 ◽  
Vol 2015 ◽  
pp. 1-14
Author(s):  
Baoyan Zhu ◽  
Jingjun Zhang ◽  
Daqing Zhang ◽  
Aibin Liu
Keyword(s):  
Closed System ◽  
Finite Time ◽  
Controller Design ◽  
Fuzzy Model ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Time Interval ◽  
Impulsive Behavior ◽  
Finite Time Interval ◽  
Delay Dependent

Delay-dependent finite-timeH∞controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-timeH∞controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds theH∞performance to a prescribed disturbance attenuation levelγ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI). Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve aH∞performance level.

scholarly journals Finite-Time Stability Analysis for a Class of Continuous Switched Descriptor Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Pan Tinglong ◽  
Yang Kun ◽  
Shen Yanxia ◽  
Gao Zairui ◽  
Ji Zhicheng
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Interval ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability has more practical application values than the classical Lyapunov asymptotic stability over a fixed finite-time interval. The problems of finite-time stability and finite-time boundedness for a class of continuous switched descriptor systems are considered in this paper. Based on the average dwell time approach and the multiple Lyapunov functions technique, the concepts of finite-time stability and boundedness are extended to continuous switched descriptor systems. In addition, sufficient conditions for the existence of state feedback controllers in terms of linear matrix inequalities (LMIs) are obtained with arbitrary switching rules, which guarantee that the switched descriptor system is finite-time stable and finite-time bounded, respectively. Finally, two numerical examples are presented to illustrate the reasonableness and effectiveness of the proposed results.

State-energy-constrained controller design for uncertain semi-state systems and its application in mechanical system control

2019 ◽  
Vol 233 (14) ◽  
pp. 4850-4862
Author(s):  
Yuanchun Ding ◽  
Falu Weng ◽  
Feiyue Geng
Keyword(s):  
Mechanical System ◽  
Finite Time ◽  
State Energy ◽  
Controller Design ◽  
Mechanical Systems ◽  
Time Interval ◽  
System Control ◽  
Sampled Data ◽  
Finite Time Interval ◽  
Energy Constrained

The state-energy-constrained controller design for uncertain semi-state systems and its application in mechanical system control is studied in this paper. The objective is to get a sampled-data-based controller, with which the system is state-energy-constrained in a finite-time interval and has a given anti-disturbance performance. First, by adopting the matrix convex sets and data sampling, a sampled-data-based model for uncertain semi-state systems is obtained. Second, by considering those state-energy-constraints in real systems, the finite-time stability theory is utilized in the system analysis, and some sufficient conditions are achieved for uncertain semi-state systems with sampled data to be stabilizable. If these conditions are solvable, the sampled-data-based state-feedback controller can be gotten, such that the controlled system has an H-infinite performance, and the state energy is constrained in a finite-time interval. Finally, the obtained theorem is used to control some mechanical systems, and the results show that the controller obtained by the theorem in this paper can effectively attenuate the vibration of those mechanical systems and constrains their state-energies in a finite-time interval.

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

scholarly journals Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Liang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markovian Jumping ◽  
Stochastic Boundedness ◽  
Partly Unknown Transition Probabilities ◽  
Finite Time Boundedness

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.

On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval

2011 ◽  
Vol 34 (7) ◽  
pp. 841-849 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Non Linear ◽  
Robust Controllability ◽  
Jump Systems ◽  
Takagi Sugeno

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches.

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