Robust H_âˆžControl And Filtering Of Stochastic TimeDelay Systems  Posted on:20140213  Degree:Doctor  Type:Dissertation  Country:China  Candidate:W H Mao  Full Text:PDF  GTID:1228330401960211  Subject:Control theory and control engineering  Abstract/Summary:  PDF Full Text Request  It is well known that timedelays, parameter uncertainties and stochastic perturbation are frequently encountered in various practical and engineering fields. These factors are usually the source of instability and degradation in control systems. Therefore, one has to consider the effect of timedelays, parameter uncertainties and stochastic perturbation when modeling the systems. Plentiful results have been reported on control theory for stochastic delayed system, however, there remain many open but challenging problems.Based on the knowledge of stochastic analysis and LyapunovKrasovskii functional theory, by linear matrix inequality technique etc., this thesis focuses on stability analysis, robust control and filtering problem for several kinds of stochastic timedelay systems. The main results obtained in this thesis are as follows:1. The problem of robust mixed H2/Hâˆžguaranteedcost control for uncertain neutral stochastic distributed timedelay systems (UNSDDS) is investigated. By Ito formulation, crossterms bounding technique, Jensen inequality, GronwallBellman inequality and LMI approach etc., LyapunovKrasovskii functionals are constructed to establish a linear stochastic bounded real lemma, by which delaydependent conditions for the solvability of the robust mixed H2/Hâˆžguaranteedcost control problem are proposed, and the robust mixed H2/Hâˆžguaranteedcost controllers are designed to guarantee the loop systems are meansquare exponentially stable for all admissible uncertainties with zero disturbance input. The timevarying delays considered include neutral delay, discrete delay and distributed delay, which may be equal to each other or not. Numerical examples are presented to show the effectiveness of the results and very the H2ã€Hâˆžperformances.2. By Ito formulation, crossterms bounding technique, Jensen inequality, GronwallBellman inequality and LMI approach etc., LyapunovKrasovskii functionals are constructed and freeweighting matrices are introduced to study robust H2/Hâˆžfiltering problems for uncertain stochastic timedelay systems (USDS) and uncertain neutral stochastic distributed timedelay systems. According to HamiltonJacobyIssac condition, complete square method is applied to derive linear stochastic bounded real lemmas for uncertain stochastic timedelay systems, by which delaydependent conditions for the solvability of the robust H2/Hâˆžfiltering problems are proposed, and the robust H2/Hâˆžfilters are designed to guarantee the filtering error systems are globally asymptotically stable in probability for all admissible uncertainties with zero disturbance input. Based on linear stochastic bounded real lemmas for uncertain stochastic timedelay systems established for uncertain neutral stochastic distributed timedelay systems, delaydependent conditions for the solvability of the robust H2/Hâˆžfiltering problems are proposed, and the robust H2/Hâˆžfilters are designed to guarantee the filtering error systems are meansquare exponentially stable for all admissible uncertainties with zero disturbance input. The delays considered are interval timevarying, and the restriction that the upper bound of the delay derivative is less than1is removed by introducing freeweighting matrices. The new LyapunovKrasovskii functional takes into account the information of the timevarying delay, the upper and lower bounds of the timevarying delay. Numerical examples are given to illustrate the effectiveness of the results.3. The delaydependent meansquare exponential stability problems of uncertain neutral stochastic distributed timedelay systems and uncertain stochastic timedelay systems are investigated. By Ito formulation, crossterms bounding technique, Jensen inequality, GronwallBellman inequality and LMI approach etc., LyapunovKrasovskii functionals are constructed and freeweighting matrices are introduced to obtain delaydependent meansquare exponential stability condition for uncertain neutral stochastic distributed timedelay systems. Numerical examples are proposed to show that the results improve some existing ones. By LyapunovKrasovskii theory and LMI method, under the generalized Finsler lemma (GFL) framework, delaydependent meansquare exponential stability criteria are established without involving any model transformation, Jensen inequality or additional freeweighting matrix. Moreover, GFL is also employed to obtain stability criteria for a class of uncertain linear stochastic neutral systems with different discrete and neutral delays. Numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing ones. The delays considered are interval timevarying, and the restriction that the upper bound of the delay derivative is less than1is removed by introducing freeweighting matrices or applying GFL. The new LyapunovKrasovskii functional takes into account the information of the timevarying delay, the upper and lower bounds of the timevarying delay.4. The problems of robust Hâˆždynamic output feedback control and filtering for uncertain I totype stochastic Markovian jump systems with unknown nonlinearities satisfying linear Lipchiz growth condition and interval modedependent timevarying delays is investigated. The aim of this problem is to design a Markovian jump exponential filter such that the filtering error system is robustly stochastically exponentially meansquare stable for a prescribed Hâˆždisturbance attenuation level. By LyapunovKrasovskii theory and generalized Finsler lemma (GFL), novel delayrangedependent and delayderivativedependent sufficient conditions are obtained to guarantee the existence of desired exponential Hx filter, which can be constructed by solving simultaneous Linear matrix inequalities (LMIs). Neither model transformations nor freeweighting matrices are involved, therefore, conservatism and computation burden result from them can be avoided. Furthermore, the usual assumption that the derivatives of the timevarying delays are less than1is removed due to the applying of GFL. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.5. The robust mixed H2/Hâˆžglobal linearization filtering problem for a general nonlinear stochastic system with interval timevarying delay and exogenous disturbance is studied. For a general nonlinear stochastic system with exogenous disturbance, although the robust Hâˆžfilter can be obtained by solving a secondorder nonlinear HamiltonJacobi inequality (HJI), it is difficult to solve the secondorder nonlinear HJI except those special cases. Based on the global linearization scheme and LyapunovKrasovskii functional theory, a stochastic bounded real lemma is established, by which the robust Hâˆžglobal linearization filter design for the nonlinear stochastic timevarying delay system is proposed via solving simultaneous linear matrix inequalities (LMIs) associated with the filtering problem in linear stochastic timevarying delay systems at vertices instead of solving the HJI associated with the Hâˆžfiltering problem in the nonlinear stochastic timevarying delay system. When the worst case disturbance attenuation of Hâˆžfiltering is considered, the mixed H2/Hâˆžfilter design problem is also solved from the H2suboptimal estimation point of view. A simulation example is provided to illustrate the effectiveness of the proposed method.Finally, the conclusions are summarized and the directions of future studies are proposed.  Keywords/Search Tags:  Ito stochastic system, (interval) timevarying delay, neutral system, LyapunovKrasovskii functional, delaydependent, globally asymptotically stable in probability, meansquare exponentially stable, robust H2/Hâˆžcontrol and filtering, Markovian jump  PDF Full Text Request  Related items 
 
