Fuzzy Static Output Feedback <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control for Nonlinear Systems Subject to Parameter Uncertainties

This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities (LMIs). LMI-based stability conditions for interval type-2 fuzzy static output feedback H_∞ control synthesis are also developed. Several simulation examples are given to show the superiority of the proposed approach.     

Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.     

H_∞ Control for Nonlinear Stochastic Markov Systems with Time-Delay and Multiplicative Noise

This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input-and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities(HJIs), the exponential mean square H_∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly,by using fuzzy T-S model approach, the H_∞ controller can be designed via solving a set of linear matrix inequalities(LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.     

Sampled-Data H∞ Dynamic Output Feedback Controller Design for Fuzzy Markovian Jump Systems

This paper considers the issue of H_∞ dynamic output feedback controller design for T-S fuzzy Markovian jump systems under time-varying sampling with known upper bound on the sampling intervals. The main aim is to realize sampled-data fuzzy dynamic output feedback control so as to demonstrate the stochastic stability and H_∞ performance index of the closed-loop sampled-data fuzzy Markovian jump systems. Then, by making the most of the information within the sampling interval,...     

Robust H_2/H_∞ Fuzzy Filtering for Nonlinear Stochastic Systems with Infinite Markov Jump

Robust fuzzy filterings for a class of nonlinear stochastic systems with infinite Markov jump are explored based on T-S fuzzy model approach in this paper. First of all, the exponentially mean square stable filter with a prescribed H∞ performance is designed via linear matrix inequalities(LMIs). Secondly, H2/H∞ fuzzy filtering is solved in terms of LMIs by minimizing the estimation error energy under the worst case fuzzy disturbance. The corresponding fuzzy filter parameters can be received by convex optimization algorithms. And lastly, two illustrative examples are performed to manifest the validity of the proposed methods.     

Robust H_∞ Control of Switched Nonlinear Systems Under Sampled Data

This paper investigates the globally asymptotically stable and L₂-gain of robust H∞ control for switched nonlinear systems under sampled data. By considering the relationship between the sampling period and the dwell time, the non-switching and one switching are discussed in the sampling interval, respectively. Firstly, a state feedback sampled-data controller is constructed by the back-stepping method, and the switching converts to asynchronous switching if it happens within the samp...     

A Robust Output—Feedback Controller for a Class of Uncertain Nonlinear Systems

1　IntroductionRecently,the nonlinear output- feedback control problems are solved successfully by usingbackstepping for a class of nonlinear systems. The partialstate feedback control problemsolved in Jiang and Praly,1996 is more general than the output- feedback control problem.However,the assumptions made in the paper are too restrictive which does not only re-quire the existence of c,γ andψ1 to be ascertained a priori,but also require them to beknown for an unknown system. If c,γ can n…     

H_2/H_∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching

In this paper, a stochastic H_2/H_∞ control problem is investigated for Poisson jumpdiffusion systems with Markovian switching, which are driven by a Brownian motion and a Poisson random measure with the system parameters modulated by a continuous-time finite-state Markov chain.A stochastic jump bounded real lemma is proved, which reveals that the norm of the perturbation operator below a given threshold is equivalent to the existence of a global solution to a parameterized system of Riccati type differential equations. This result enables the authors to obtain sufficient and necessary conditions for the existence of H_2/H_∞ control in terms of two sets of interconnected systems of Riccati type differential equations.     

Robust H_∞ Control for Uncertain Markovian Jump Linear Time-Delay Systems

1 ＩＮＴＲＯＤＵＣＴＩＯＮＭａｒｋｏｖｉａｎｊｕｍｐｓｙｓｔｅｍｓａｒｅｄｅｆｉｎｅｄａｓａｆａｍｉｌｙｏｆｌｉｎｅａｒｓｙｓｔｅｍｓｗｉｔｈＭａｒｋｏｖｉａｎｊｕｍｐｐａｒａｍｅｔｅｒｓ.Ｔｈｉｓｃｌａｓｓｏｆｓｙｓｔｅｍｓ,ｗｈｉｃｈｗｅｒｅｉｎｉｔｉａｌｌｙｉｎｔｒｏｄｕｃｅｄｂｙＫｒａｓｏｒｋｉｉａｎｄＬｉｄｓｋｉｉｉｎｒｅｆｅｒｅｎｃｅ [1 ],ａｒｅａｌｗａｙｓｕｓｅｄｔｏｍｏｄｅｌｔｈｅｐｌａｎｔｓｗｈｏｓｅｓｔｒｕｃｔｕｒｅｉｓｓｕｂｊｅｃｔｔｏｒａｎｄｏｍｌｙａｂｒｕｐｔｃｈａｎｇｅ…     

Robust H_∞ Control with Exponent Stability for Time-Delay Uncertain Systems

1 .ＩＮＴＲＯＤＵＣＴＩＯＮＩｔｉｓｗｅｌｌ ｋｎｏｗｎｔｈａｔｔｈｅｓｔａｂｉｌｉｚａｔｉｏｎｏｆｔｈｅｓｙｓｔｅｍｓｗｉｔｈｔｉｍｅｄｅｌａｙｓｉｎｄｉｆｆｅｒｅｎｔｓｔａｔｅｓｉｓａｔｏｕｇｈｐｒｏｂｌｅｍｂｅ ｃａｕｓｅｔｈｅｔｉｍｅｄｅｌａｙｓｉｎａｓｙｓｔｅｍｍａｙｉｎｄｕｃｅａｎｉｎｓｔａｂｉｌｉｔｙｏｆｔｈｅｐｅｒｆｏｒｍａｎｃｅｓｏｆｔｈｅｃｌｏｓｅｄ ｌｏｏｐｓｃｈｅｍｅｓ.Ｔｈｅｒｅｆｏｒｅ,ｔｈｅｓｕｂｊｅｃｔｏｆｓｔａｂｉｌｉｔｙａｎｄｃｏｎｔｒｏｌｆｏｒｔｉｍｅ ｄｅｌａｙ…     

State and Output Feedback Finite-time Guaranteed Cost Control of Linear It Stochastic Systems

The problem of guaranteed cost control based on finite-time stability for stochastic system is first investigated in this paper.The motivation of solving this problem arises from an observation that finite/infinite-horizon guaranteed cost control does not consider the transient performance of the closed-loop system,but guaranteed cost control based on finite-time stability involves this practical requirement.In order to explain this problem explicitly,a concept of the stochastic finite-time guaranteed cost control is introduced,and then some new sufficient conditions for the existence of state and output feedback finite-time guaranteed cost controllers are derived,which guarantee finite-time stochastic stability of closed-loop systems and an upper bound of a quadratic cost function.Furthermore,this problem is reduced to a convex optimization problem with matrix inequality constraints and a new solving algorithm is given.Finally,an example is given to illustrate the effectiveness of the proposed method.     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

Nonlinear H_∞ filtering for interconnected Markovian jump systems

1.INTRODUCTIONState esti mation or observer design has been an i m-portant research topic and has been widely used incontrol and signal processing in the last fewdecades[1~3].One of the esti mation approaches isKal man filtering,which is based on the assumptionthat the system model under considerationis availableandits disturbances are Gaussian noises with knownstatistics.However,the noise sources may not be ex-actly known and uncertainties may appear.There-fore,an alternative esti matio…     

On the H_∞ Control for Linear Time-Delay Systems

1.INTRODUCTIONTheH∞controllerdesignmethodhasreceivedmuchattentioninthelastdecade,andmanyPapersonfindingtheH∞controllerfornondelayedlinearsystems(includingthecase:withsomenorm-boundeduncertainty)hasbeenpublished[5-11].However,onlyafewpapersonthedelayedlinearsystemsanduncertaindelayedlinearsystemsexist[l~4].Ontheotherhand,thetime-delayisfrequentlyacauseofinstability,thusthestabilizationandHadcontrolsynthesisoftime-delaylinearsystemsareneededinpractice.Inthispaper,firstlyswegivetwoRiccat…     

The Optimal Control for the Output Feedback Stochastic System at the Risk-Sensitive Cost

Abstract: The optimal control of the partially observable stochastic system at the risk-sensitive cost is considered in thispaper. The system dynamics has a general correlation between system and measurement noise. And the risk-sensitive costcontains a general quadratic term (with cross terms and extra linear terms). The explicit solution of such a problem ispresented here using the output feedback control method. This clean and direct derivation enables one to convert suchpartial observable problems into the equivalent complete observable control problems and use the routine ways to solvethem.     

Sliding Mode Control to Stabilization of an ODE-Schrdinger Cascade Systems Subject to Boundary Control Matched Disturbance

This paper is concerned with the boundary feedback stabilization of a coupled ODESchr¨odinger system cascades with the external disturbance flowing the control end. The author uses the sliding mode control(SMC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the reaching condition is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. Some numerical simulations is presented to illustrate the effectiveness of the proposed control.     

New Results on H_∞ Control of Linear Systems with Interval Time-Varying Delays

This paper is focused on the H_(∞) control problem for linear systems with interval timevarying delays.By employing a reciprocally convex combination approach and a delay decomposition approach,some new delay-dependent bounded real lemmas(BRLs) are derived such that the closedloop system is asymptotically stable with a prescribed H_(∞) level.The BRLs are then used to solve the H_(∞) controller design by incorporating with the cone complementary approach.Three numerical examples are finally given to show the validity of the proposed method.     

Macro-economic Model and Its H_∞ Control Strategies for Liaoning Province

1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒａｂｌｅｒｅｓｅａｒｃｈｅｓｈａｖｅｂｅｅｎｍａｄｅｏｎｍａｃｒｏｅｃｏｎｏｍｉｃｍｏｄｅｌｓｔｉｌｌｎｏｗ .Ｐｏｌｉｃｙｍａｋｅｒｓｕｓｕ ａｌｌｙｐｒｅｄｉｃｔａｎｄａｎａｌｙｚｅｅｃｏｎｏｍｉｃｓｉｔｕａｔｉｏｎ ,ｍａｋｅｅｃｏｎｏｍｉｃｄｅｃｉｓｉｏｎｓｂａｓｅｄｏｎｔｈｅｓｅｍｏｄｅｌｓ[1] .Ｔｅｃｈｎｉｑｕｅｓｕｓｅｄｉｎｄｅｃｉｓｉｏｎｐｒｏｂｌｅｍａｎｄｒｉｓｋｍａｎａｇｅｍｅｎｔｕｓｕａｌｌｙａｒｅｏｐｔｉｍａｌｒｅｇｕｌａｔｏｒｔｈｅ…     

Variable Structure Control of Distributed Parameter Systems and Application to the System of Heat Process

ＶａｒｉａｂｌｅＳｔｒｕｃｔｕｒｅＣｏｎｔｒｏｌｏｆＤｉｓｔｒｉｂｕｔｅｄＰａｒａｍｅｔｅｒＳｙｓｔｅｍｓａｎｄＡｐｐｌｉｃａｔｉｏｎｔｏｔｈｅＳｙｓｔｅｍｏｆＨｅａｔＰｒｏｃｅｓｓＺＨＡＯＷｅｎｒｏｎｇＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ...     

A Family of Reliable H_∞ State-Feedback Controllers for Nonlinear Systems with Strictly Redundant Actuators: the Full Information Case

1　 IntroductionInherited from state space linear H∞ control theory,a number of nonlinear H∞ solutionshave been presented in terms of various formulations.The nonlinear H∞ control problemcan be stated as follows:find a compensator,either state feedback ormore general outputfeedback such that( 1 ) the internal state of the closed-loop system is stable and( 2 ) the L2 -gain of the mapping from the exogenous input disturbance to the controlled output liketracking error or cost variables is mi…