Stability Analysis And Control For A Class Of T-S Model Based2-D Systems

This dissertation mainly discusses the problem of stability analysis, controller design and filtersynthesis for a class of two dimensional systems based on the commonly used T-S model. Consideringthe stability and H∞performance analysis problem for a class of T-S model based two dimension-al systems with parametric uncertainties. For the2-D control problem, State feedback and outputfeedback controller are designed that the closed-loop systems are asymptotically stable and has a pre-scribed H∞performance. A typical H∞filtering problem is concerned that the l2-induced gain fromthe noise input signal to the estimation error is less than a prescribed level. The primary results of thispaper contains the following three parts.The first part is concerned with the stability and H∞performance analysis problem for a class ofT-S model based two dimensional systems with parametric uncertainties. In two dimensional systems,the system information is propagated along two independent directions. By taking this structuralfeature into consideration, dividing the Lyapunov function into two directions, we extend the1-Dresult to the2-D case. The uncertainty is assumed to be of structured linear fractional form, theH∞performance analysis problem is facilitated by introducing some additional instrumental matrixvariables. By using basis-dependent Lyapunov function, a less conservative condition is obtained thatthe two dimensional system is asymptotically stable and has a prescribed H∞performance.In the second part, we discussed the stabilization problem of a class of T-S model based t-wo dimensional fuzzy systems. State feedback and output feedback controller are designed that theclosed-loop system are asymptotically stable and has a prescribed H∞performance. A state feedbackcontroller is obtained by using PDC approach. Then analyze the H∞performance of the obtainedclosed-loop system, by using Schur complements and adding slack matrices combined with the s-caling techniques of inequalities, the coexists of Lyapunov function matrices and it’s inverse areshuned. Feedback matrices, system matrices and previous slack matrices are decoupled by using ma-trix transformation skills and adding new slack matrices. The controller can be solved based on thematrix inequalities. By using matrix’s singular value decomposition (SVD) technics combined withthe method we used in the design of state output feedback controller, an efficient LMI-based approachis proposed for output feedback controller. Numerical examples are given to illustrate the validity ofour design.In the third part, we investigated the H∞filtering problem of two dimensional fuzzy systems.Attention is focused on the design of a T-S based fuzzy filter such that the filter error systemis asymptotically stable and preserves a prescribed H∞performance. By using basis-dependent Lyapunov function and adding slack matrix variables, the coupling between the Lyapunov matricesand the filter system matrices is eliminated. A linear matrix inequality is obtained for design the H∞fuzzy filter. Finally, an numerical example is given to validate the proposed approach.