Model Reduction And Reduced-Order Filter Design For Discrete-Time T-S Fuzzy Systems

Model reduction and filtering design are major problems in system and control areas. Model reduction can reduce the systems complexity, improve the systems response speed. Filtering can assume the inner immeasurable signal basing on the measurable output, solve the inner parameter unmeasured problem.T-S fuzzy systems can approach complex nonlinear systems by fuzzy rules, using linear multinomial describe a complex systems. So it is signify to research the T-S fuzzy systems. Heretofore, it is lacking of research method to solve model reduction and filter-ing design problem, especially there are delay of signal transmission, external stochastic disturbance, singularity in the systems.Based on the background of mention above, this paper mainly investigates the re-search of discrete-time T-S fuzzy systems, focused on the delay, singularity and stochas-tic disturbance, obtain the method of model reduction and filtering design under those infection.First, based on the research object:discrete-time T-S fuzzy time-delay systems, discrete-time T-S fuzzy time-delay singularity systems and discrete-time T-S fuzzy ran-dom systems, stability analysis has been research. Construction of quadratic Lyapunov-Krasovskii equation aim at delay-dependent and delay-independent respectively. Taking advantage of stochastic disturbance mathematical expectation, remove the stochastic dis-turbance item in the Lyapunov criterion. By the mean of Schur complement and matrix transformation, transform the sufficient condition into linear inequality restrain, what can be solved by Matlab. Through numerical example show the influence of delay, singular and stochastic disturbance, the result proved the validity of stability criterion.Second, on the basic of system stability research, put forward the model order reduc-tion method of T-S fuzzy systems. Based on the discrete T-S fuzzy time-delay systems, Hankel norm model order reduction is researched. As a result of the existence of time delay, the reduced order model of error system asymptotic stability criterion of conser-vatism. Making use of delay partitioning, big delay d has been partitioned into m period small delay tau, which making the delay dependent stability condition is based on small delay tau function, a reduced order model which reduces the error system with time-delay dependent on the conservatism of the asymptotic stability criterion. Based on the convex linearization method to build the Hankel norm sense, the parameters of reduce order mod-el can be obtained by solving the linear inequalities. Through numerical example proved the validity of the model order reduction method, and verifies the reduced order model of higher order Hankel norm, which is fit with the actual situation.Third, this paper put forward the design method of filters with discrete T-S fuzzy sys-tem. In this chapter, using discrete T-S fuzzy singular time-delay systems as the research object, has carried on the H∞filter design research. Due to the fact that the delay may be changed in engineering system, described delay as the time delay function between the minimum delay and maximum time delay, build a new delay function of Lyapunov-Krasovskii functional form, which reduce the time delay filter error system relies on the conservatism of the asymptotic stability criterion. Free full matrix method is used to de-sign the discrete T-S fuzzy singular systems with time-delay H∞filter, and by solving the linear matrix inequality (LMI) obtain H∞filter parameters. Through numerical simulation example illustrates the feasibility of filter design method.Fourth, based on the discrete T-S fuzzy stochastic systems, reduced order l2-l∞filter has been research. Using matrix partition and convex linear method, full order l2-l∞filter of discrete T-S fuzzy system is designed. And by introducing a backlog matrix W in the partitioned matrix, get the system all order l2-l∞filter parameters when W=I. This paper give out of the reduced order filter design method based on projection theorem. Finally, a numerical example shows that the l2-l∞filter design method is feasible, the numerical example results show that the high order filter has better l2-l∞performance.Finally, in view of the hypersonic aircraft for fuzzy modeling and filter system de-sign, implementation of hypersonic flight vehicle’s internal state. First of all, using the fuzzy rules of fuzzy identification system of hypersonic flight vehicle model, and setting an optimal index, using the optimal modeling method for hypersonic flight vehicle fuzzy modeling; then, fuzzy observe which meet the performance requirements has been de-signed by the method of proposed filter designed. Through numerical simulation example shows that fuzzy observer of the tracking error satisfies the requirement of system, which shows the effectiveness of the filter design method of this study, can be applied in the actual engineering system.This article research results for solving vehicle control problem, including hyper-sonic flight vehicle observer and aerospace nonlinear system, provides technical basis for systems simplify and filter design problem, research how to reduce the signal transmis- sion delay in practical systems, the effects of external random disturbance and singularity, have certain theoretical analysis and reference value for engineering applications.