Study On Estimation Method For A Class Of Switched Linear Systems State

As a class of important hybrid system, switched system has attracted more and more attentions. Now state estimation of switched system is the key research point in the literature. Under current conditions, on the one hand, because of the technology and economy constraints, the dimension of the system output vector is always less than the dimension of systems state, which makes system measurement information incomplete. On the other hand, the control of the system, system modeling and identification, etc, need to estimate the unknown system state. Therefore, state estimation of switched system is studied in this dissertation, and the main contents are as follows:With the unknown switching times, unknown active subsystem at every moment and the full rank of state matrix difference between the subsystems of switched systems, the state estimation in this dissertation has extensively studied and improved for the autonomous switched systems using ALIEN algebraic approximation, which improves estimation accuracy and reduces the complexity of estimation. First of all, with switching times unknown, the impulsive model is introduced. By using the properties of smooth function and convolution, unknown initial value and the difference effect of the system will be eliminated. The algebraic expression of switching times is obtained. Then, on the basis of this result, activated subsystem at the moment is deduced. The existing approachs are available for the current active subsystem state estimation. Finally, through a numerical example, the proposed method which has estimation accuracy and effciency was tested and verified by Matlab simulation.On the basis of research results for switched system with two subsystems, the number of observers was deduced for switched system with multi-subsystems. This dissertation studies and designs state estimation approach for these systems. First of all, by using the ALIEN method, the algebraic expression of switching times which contains only the known or measured signals is obtained under the multiple parallel observations. Then, based on these, the effective approach of multi-subsystems state estimation is proposed for linear switched systems. Lastly, through a numerical example, the proposed state estimation method was verified by Matlab simulation program. It has high speed, low cost, high precision advantages.For the non-full rank of the state matrix difference between the subsystems of systems, with the unknown dynamic performance of the subsystem, the effective approach of state estimation for the system is proposed. By using ALIEN method, the algebraic expression of switching time for the non-full rank of the state matrix between the subsystems is obtained. According to the estimated dynamic performance of the subsystem, system state can be estimated. Through a numerical example, the proposed method which is accurate and effective was tested and verified by Matlab simulation.