Analysis And Synthesis Of Singular Systems With Time Delay  Posted on:20120810  Degree:Doctor  Type:Dissertation  Country:China  Candidate:Z G Wu  Full Text:PDF  GTID:1118330332478374  Subject:Control Science and Engineering  Abstract/Summary:  PDF Full Text Request  Singular systems can better describe some practical systems than statespace ones. On the other hand, time delays are often encountered in many control systems, and lead to the instability and degradation in control performance of control systems. Meanwhile, much attention has been paid to Markovian jump systems due to the fact that they have important practical applications. Thus, the study on singular systems with time delay and singular Markovian jump systems with time delay is important both in theory and in practice, and is of great interest to lots of researchers.In terms of linear matrix inequality approach, the problems of stability analysis, Hâˆžcontrol,Hâˆžfiltering and l2lâˆžfiltering are studied for singular (Markovian jump) systems with time delay. The main contents obtained in this dissertation are as follows:1. The Hâˆžcontrol problem for singular systems with time delay is discussed in terms of linear matrix inequality approach. A delaydependent sufficient condition is presented to ensure the system to be admissible with a prescribed Hâˆžperformance index via an augmented Lyapunov functional. Based on the condition, the design method for the Hâˆžstate feedback controller is presented.2. The problem of delaydependent Hâˆžfiltering is considered for singular systems with timevarying delay. A filter is designed to guarantee the filtering error system to be exponentially admissible with a prescribed Hâˆžperformance level. The design method of the filter is given, which is based on the strict linear matrix inequalities.3. The stability analysis problem is investigated for discretetime singular systems with timevarying delay. In terms of linear matrix inequality approach, a delaydependent sufficient condition is obtained to guarantee the system to be regular, causal and stable. The proposed result has less conservatism than the existing one. 4. The problem of delaydependent Hâˆžcontrol is considered for singular Markovian jump systems with time delay. A delaydependent sufficient condition is obtained to guarantee the system to be stochastically admissible with a prescribed Hâˆžperformance level in terms of freeweighting matrix method. Based on the condition, the design method of the desired Hâˆžstate feedback controller is given. Numerical examples show the less conservatism of the proposed methods.5. The problem of Hâˆžfiltering is considered for singular Markovian jump systems with time delay. A sufficient condition is obtained to guarantee the system to be stochastically admissible with a prescribed Hâˆžperformance level in terms of Jensen integral inequality. The delayindependent and delaydependent conditions are proposed for the exist of the modeindependent filter. The design method of the desired filter is also given. Numerical examples are given to demonstrate that the given results have less conservatism than the existing ones.6. The problem of l2lâˆžfiltering is considered for discretetime singular Markovian jump systems with timevarying delays. In terms of delay partitioning method, a delaydependent sufficient condition is obtained to guarantee the system to be stochastically admissible with a prescribed l2lâˆžperformance level. The condition is given for the exist of the modeindependent filter, and the design method of the desired filter is also given.Finally, the conclusion and further research topics are given.  Keywords/Search Tags:  singular systems, time delay systems, Markovian jump systems, admissibilty, H_âˆžcontrol, H_âˆžfiltering, l2â€”lâˆžfiltering, linear matrix inequality  PDF Full Text Request  Related items 
 
