Prescribed Hinfin Performance Research Articles

LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

Robust Stability Analysis and Feedback Control for Uncertain Systems With Time-Delay and External Disturbance

This article addresses the delay-dependent Takagi–Sugeno (T–S) fuzzy state feedback control and exponential admissibility analysis for a class of T–S fuzzy singular uncertain systems. First, the T–S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input, and unmatched disturbance. Second, the delay-dependent T–S fuzzy state feedback controller is designed by employing the T–S fuzzy model. Third, the free-weighting matrices and delay-dependent Lyapunov–Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T–S fuzzy state feedback controller is designed for the T–S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods.

LMIs-based stability analysis and fuzzy-logic controller design for networked systems with sector nonlinearities: Application in tunnel diode circuit

In this article, the problem of exponential mean-square stability analysis is discussed for uncertain networked control systems expressed by a stochastic T-S fuzzy model. In general, the characteristics of random occurrence for multipath packet dropouts often exist in the signal transmission network. For dealing with this difficult point, a dynamic output feedback strategy combining stochastic Bernoulli theory is employed. Then, delay-dependent stability conditions are derived and closed-loop system is exponentially mean-square stable by designing fuzzy-basis-dependent Lyapunov functional. Furthermore, in terms of linear matrix inequalities (LMIs) technology, sufficient conditions are gained to guarantee the prescribed H-infinity performance. Different from previous literatures, the congruence transformation method is employed to determine controller gain matrices for reducing the computation complexity of solving LMIs. Finally, the proposed method is applied in tunnel diode circuit model to verify the applicability.

Robust Stability Analysis and Feedback Control for Uncertain Systems with Time-Delay and External Disturbance

This paper addresses the delay-dependent Takagi-Sugeno (T-S) fuzzy state feedback control and exponential admissibility analysis for a class of T-S fuzzy singular uncertain systems. Firstly, the T-S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input and unmatched disturbance. Secondly, the delay-dependent T-S fuzzy state feedback controller is designed by employing the T-S fuzzy model. Thirdly, the free-weighting matrices and delay-dependent Lyapunov-Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T-S fuzzy state feedback controller is designed for the T-S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods.

Robust stability analysis and feedback control for networked control systems with additive uncertainties and signal communication delay via matrices transformation information method

The interval type-2 Takagi-Sugeno (T-S) fuzzy dynamic output feedback and H-infinity stability analysis is studied for a class of networked control systems with multiple time-varying additive uncertainties, time-varying signal communication delay and external disturbance. Firstly, the interval type-2T-S fuzzy is employed to denote the system plant. Secondly, the multiple time-varying additive uncertainties are introduced in the controller design and the state variables depending on additive uncertainties. Thirdly, the delay-dependent Lyapunov-Krasovskii functional with double integral terms is designed to derive the less conservative stability conditions in terms of linear matrix inequalities (LMIs). The characteristic of the state variables are reflected effectively by employing the controller with multiple time-varying additive uncertainties. The closed-loop system is asymptotically stable with prescribed H-infinity performance index γ by employing the matrices transformation information. The less conservative stability conditions are derived and extended into the networked control system without additive uncertainties. Finally, simulations are presented to show the effectiveness of the proposed methods.

Stability analysis and output feedback control for stochastic networked systems with multiple communication delays and nonlinearities using fuzzy control technique

This paper addresses the H-infinity Takagi-Sugeno (T-S) fuzzy control for a class of T-S fuzzy discrete networked control systems with random interval communication delays and random sector nonlinearities. Firstly, the T-S fuzzy model is employed to approximate the discrete networked control system and the ℓth-order Rice fading channels model is introduced in the system model. Secondly, the T-S fuzzy dynamic output feedback controller with ℓth-order Rice fading channels output is designed for the T-S fuzzy discrete networked control system. Thirdly, the discrete delay-dependent Lyapunov-Krasovskii functional, stochastic system theory and Bernoulli probability distribution are employed to derive the stability conditions in terms of linear matrix inequalities (LMIs). Compared with previous works, the fading channels in the signal transmission are described clearly by setting the different channels coefficients of the ℓth-order Rice fading channels model. The closed-loop system is exponentially mean-square stable and prescribed H-infinity performance is guaranteed by designing the T-S fuzzy dynamic output feedback controller. The factorizations in the polynomial and the congruence transformation matrices are introduced to solve the LMIs, such that the controller gain matrices are determined. Finally, simulation examples are presented to show the effectiveness of proposed methods.

H-infinity stability analysis and output feedback control for fuzzy stochastic networked control systems with time-varying communication delays and multipath packet dropouts

The H-infinity stability analysis and delay-dependent Takagi–Sugeno (T–S) fuzzy dynamic output feedback control are proposed for the T–S fuzzy discrete networked control systems with time-varying communication delay and multipath packet dropouts. T–S fuzzy model is employed to approximate the discrete networked control system with time-varying state delay and external disturbance. Stochastic system theory and Bernoulli probability distribution are employed to describe the time-varying communication delay and multipath packet dropouts. Delay-dependent T–S fuzzy dynamic output feedback controller is designed. The delay-dependent T–S fuzzy dynamic output feedback controller is employed to relax the design conditions and enhance the design flexibility. The delay-dependent Lyapunov–Krasovskii functional, stochastic system theory and Bernoulli probability distribution are introduced to guarantee the stochastic mean-square stability and prescribed H-infinity performance. Some slack matrices are introduced to reduce the computation complexity. Finally, simulation examples are presented to show the effectiveness and advantages of the proposed methods.

Decentralized Fuzzy $H_{\infty}$ Filtering for Nonlinear Interconnected Systems With Multiple Time Delays

In general, due to the interaction among subsystems, it is difficult to design an Hinfinity filter for nonlinear interconnected systems. This paper introduces a decentralized Hinfinity fuzzy filter design for nonlinear interconnected systems with multiple time delays via T-S fuzzy models. The T-S fuzzy model consists of N time-delay T-S fuzzy subsystems. The decentralized Hinfinity filter is designed based on this model, which the asymptotic stability and a prescribed Hinfinity performance index are guaranteed for the overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of this approach.

H<SUB align=right>∞ filtering design for network control systems with jump parameters

The problem of robust h-infinity filtering design for networked control systems with Markovian jump parameters and packets lost is considered. A wider class of parameter uncertainties than norm-bounded parameter uncertainties is described in this model. Sufficient conditions for the filter to satisfy prescribed h-infinity performance are given in terms of LMIs, which can stabilise the system and guarantee a prescribed h-infinity performance for all admissible parameter uncertainties. A numerical example is given to illustrate the feasibility and effectiveness of the developed technique.

Non-fragile state feedback H-infinity control for discrete-time systems with quantized signals

This paper presents a study on the problem of non-fragile state feedback H-infinity controller design for linear discrete-time systems with quantized signals. The quantizers considered here are dynamic and time-varying. With the consideration of controller gain variations and quantized signals at the same time, a new non-fragile H-infinity control strategy is proposed with updating quantizer’s parameters, such that the quantized closed-loop system is asymptotically stable and with a prescribed H-infinity performance bound. An example is presented to illustrate the effectiveness of the proposed control strategy.

Delay-dependent ℋ ∞ filtering for uncertain time delay nonlinear systems: an LMI approach

The problem of designing a delay-dependent robust Hinfin filter for time delay Takagi-Sugeno fuzzy models is considered. The purpose is to design delay-dependent Hinfin filters ensuring a prescribed Hinfin performance level for the estimation error, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of a delay-dependent Hinfin filter are given in terms of linear matrix inequalities. Membership functions' (MFs) structural information is incorporated into the delay-dependent filter design to reduce the conservativeness of neglecting this information. It is shown that incorporating MFs' structural information into the filter design does not lead to bilinear matrix inequalities, as in the control design case. Finally, a numerical example is used to illustrate the effectiveness of the proposed design techniques.

Reliable$rm H_infty $Fuzzy Control for Continuous-Time Nonlinear Systems With Actuator Failures

This paper is concerned with the design of reliable Hinfin fuzzy controllers for continuous-time nonlinear systems with actuator failures. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. The objective is to find a stabilizing state-feedback fuzzy controller such that the nominal Hinfin performance is optimized while satisfying a prescribed Hinfin performance constraint in the actuator failure cases. Based on the linear matrix inequality (LMI) techniques, two efficient methods for the design of a suboptimal reliable Hinfin fuzzy controller are proposed. Different Lyapunov functions are used during the design for the nominal and actuator failure cases, which lead to a less conservative controller design. In the first method, a single Lyapunov function is used for the actuator failure cases. The second method adopts a parameter-dependent Lyapunov function for the actuator failure cases, which further reduces the conservatism of the design. Finally, numerical simulations on the chaotic Rossler system are given to illustrate the effectiveness of the proposed design methods

Delay-dependent H-infinity filtering for neutral time-delay systems

This paper deals with the robust delay-dependent H-infinity filtering problem for neutral delay differential systems. The resulting filter is of the Luenberger observer type, and it guarantees that the filtering systems remains asymptotically stable and satisfies a prescribed H-infinity performance level. The Lyapunov stability theory and the descriptor model transformation are used for analysis of the system and are expected to be least conservative as compared with existing design methods. Some examples are provided to demonstrate the validity of proposed design approach.

Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements

In this paper, the robust Hinfin filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. We aim to design filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable, and the prescribed Hinfin performance constraint is met. In terms of certain linear matrix inequalities (LMIs), sufficient conditions for the solvability of the addressed problem are obtained. When these LMIs are feasible, an explicit expression of a desired robust Hinfin filter is also given. An optimization problem is subsequently formulated by optimizing the Hinfin filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

Parameter-dependent filter design with guaranteed ℋ∞ performance

In the paper, the problem of H-infinity filtering for a class of linear uncertain systems is studied. The parameter uncertainties are assumed to reside in a polytope. The paper is focused on the design of a parameter-dependent filter which guarantees the filtering error system to be asymptotically stable and has a prescribed H-infinity performance. By employing a parameterdependent Lyapunov function approach, sufficient conditions are established for the existence of the desired filters in terms of linear matrix inequalities, which can be handled easily by using the available toolbox. Both continuous- and discrete-time cases are investigated. It is shown, via a numerical example, that the proposed filter design methods are more effective and less conservative than some existing results.

Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty

This paper studies, via a linear matrix inequality approach, the problem of Hinfinity control for discrete time-delay linear systems with parametric uncertainty. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and time delay in the state. First, the problem of robust stability of the underlying system is investigated. Next, we address the problem of robust Hinfinity state feedback control in which both robust stability and a prescribed Hinfinity performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a linear matrix inequality has a symmetric positive definite solution.