scholarly journals Sufficient conditions for H-infinity control on the finite time interval

2021 ◽  
Vol 1925 (1) ◽  
pp. 012024
Author(s):  
A V Panteleev ◽  
A A Yakovleva
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Finite Time Interval ◽  
H Infinity ◽  
H Infinity Control

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.

scholarly journals New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Weiwei Zhang ◽  
Jinde Cao ◽  
Ahmed Alsaedi ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Finite Time Interval ◽  
Delayed Neural Networks ◽  
New Methods ◽  
Theoretical Results

Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order α, 0<α≤1/2 and 1/2<α<1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finite-time interval. Numerical example is given to verify the feasibility of the theoretical results.

scholarly journals Finite-Time H2/H∞ Control Design for Stochastic Poisson Systems with Applications to Clothing Hanging Device

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yan Qi ◽  
Shiyu Zhong ◽  
Zhiguo Yan
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Control Design ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Transient Performance ◽  
Definition Of

In this paper, the design of finite-time H2/H∞ controller for linear Itô stochastic Poisson systems is considered. First, the definition of finite-time H2/H∞ control is proposed, which considers the transient performance, H2 index, and H∞ index simultaneously in a predetermined finite-time interval. Then, the state feedback and observer-based finite-time H2/H∞ controllers are presented and some new sufficient conditions are obtained. Moreover, an algorithm is given to optimize H2 and H∞ index, simultaneously. Finally, a simulation example indicates the effectiveness of the results.

scholarly journals RobustL2-L∞Filtering of Time-Delay Jump Systems with Respect to the Finite-Time Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Delayed Systems ◽  
Markov Jump Linear Systems

This paper studied the problem of stochastic finite-time boundedness and disturbance attenuation for a class of linear time-delayed systems with Markov jumping parameters. Sufficient conditions are provided to solve this problem. TheL2-L∞filters are, respectively, designed for time-delayed Markov jump linear systems with/without uncertain parameters such that the resulting filtering error dynamic system is stochastically finite-time bounded and has the finite-time interval disturbance attenuationγfor all admissible uncertainties, time delays, and unknown disturbances. By using stochastic Lyapunov-Krasovskii functional approach, it is shown that the filter designing problem is in terms of the solutions of a set of coupled linear matrix inequalities. Simulation examples are included to demonstrate the potential of the proposed results.

scholarly journals Resilient - Filtering of Uncertain Markovian Jumping Systems within the Finite-Time Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shuping He
Keyword(s):  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markovian Jumping ◽  
Markovian Jumping Systems ◽  
Finite Time Boundedness

This paper studies the resilient - filtering problem for a class of uncertain Markovian jumping systems within the finite-time interval. The objective is to design such a resilient filter that the finite-time - gain from the unknown input to an estimation error is minimized or guaranteed to be less than or equal to a prescribed value. Based on the selected Lyapunov-Krasovskii functional, sufficient conditions are obtained for the existence of the desired resilient - filter which also guarantees the stochastic finite-time boundedness of the filtering error dynamic systems. In terms of linear matrix inequalities (LMIs) techniques, the sufficient condition on the existence of finite-time resilient - filter is presented and proved. The filter matrices can be solved directly by using the existing LMIs optimization techniques. A numerical example is given at last to illustrate the effectiveness of the proposed approach.

Finite time stability and comparison principles

1968 ◽  
Vol 64 (3) ◽  
pp. 749-756 ◽  
Author(s):  
A. A. Kayande ◽  
J. S. W. Wong
Keyword(s):  
Differential System ◽  
Finite Time ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Differential Inequalities ◽  
Finite Time Interval ◽  
Time Stability ◽  
Comparison Principles ◽  
Finite Time Stability

Motivated by discussion on practical stability in LaSalle and Lefschetz (3), Weiss and Infante (5), have discussed various notions of stability over finite time interval of a given differential system. This theory of stability differs from the usual stability theory mainly by the preassigned limits to which any given solution of the differential system must adhere. Sufficient conditions for these notions of stability are given in (5) in terms of certain Lyapunov-like functions satisfying some appropriate differential inequalities. The purpose of this article is to introduce some complementary notions of finite time stability and weaken the conditions on the differential inequalities involving Lyapunov-like functions by the use of comparison principles.

scholarly journals Finite-time interval observer design for discrete-time switched systems: A linear programming approach

2020 ◽  
Vol 53 (7-8) ◽  
pp. 1388-1394
Author(s):  
Fei Sun ◽  
Jun Huang ◽  
Xiang Ma ◽  
Xiao Wen
Keyword(s):  
Linear Programming ◽  
Discrete Time ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Observer Design ◽  
Programming Approach ◽  
Time Interval ◽  
Finite Time Interval ◽  
Interval Observer

This paper deals with the finite-time interval observer design method for discrete-time switched systems subjected to disturbances. The disturbances of the system are unknown but bounded. The framework of the finite-time interval observer is established and the sufficient conditions are derived by the multiple linear copositive Lyapunov function. Furthermore, the conditions which are expressed by the forms of linear programming are numerically tractable by standard computing software. One example is simulated to illustrate the validity of the designed observer.

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.

Sign in / Sign up

Export Citation Format

Share Document