With Polytopic Uncertainties Of 2-d Roesser Model Robust H2, H ¡Þ Control And Filtering

Uncertainty exists in real industrial process.The introduction of uncertainty in system describes the difference between the mathematic model and controlled plant, which reflects the existing of the variation of the system parameters and disturbance. Polytopic-type uncertainty is one of uncertainties.Using Lyapunov and LMI methods, robust control and robust filtering problems of 2-D Roesser model with polytopic uncertainties have been solved.The slack variable technique was used in the results to reduce the conservation.Firstly,a necessary condition of 2-D Roesser model with polytopic uncertainties which satisfies asymptotic stability and H₂ performance index is given.A state H₂ feedback controller is designed such that the closed-loop system is asymptotic stable and satisfies H₂ performance index.A necessary condition of 2-D Roesser with polytopic uncertainties which satisfies asymptotically stability and H_∞performance index is given.A state H_∞feedback controller and an output one are designed such that the closed-loop system is asymptotic stable and satisfies H_∞performance index.Secondly,using Lyapunov and schur complement methods,an observer-based 2-D H_∞filter is designed.Using Lyapunov and variable substitution method,necessary conditions of robust H_∞filtering and robust H₂ filtering of Roesser model with polytopic uncertainties are given.Some numerical examples are given to illustrate the feasibility and efficiency of methods proposed in the end of those two parts.At last,the problem of the guaranteed cost control 2-D Roesser model with polytopic uncertainty is studied.The quadratic performance index and the definition of guaranteed cost controller are given.A necessary condition for the existence of guaranteed cost controller is deduced based on Lyapunov theory.