Filter And Observer Design For Polynomial Discrete-Time Systems: A Sum Of Squares Based Approach - Mohd Azman, Su Noorazma (2018)
The polynomial discrete-time systems are the type of systems where the dynamics of the systems are described in polynomial forms.This system is classified as an important class of nonlinear systems due to the fact that many nonlinear systems can be modelled as,transformed into,or approximated by polynomial systems.The focus of this thesis is to address the problem of filter and observer design for polynomial discrete-time systems.The main reason for focusing on this area is because the filter and observer design for such polynomial discrete-time systems is categorised as a difficult problem.This is due to the fact that the relation between the Lyapunov matrix and the filter and observer gain is not jointly convex when the parameter-dependent or state-dependent Lyapunov function is under consideration.Therefore the problem cannot possibly be solved via semidefinite programming (SDP).In light of the aforementioned problem, we establish novel methodologies of designing filters for estimating the state of the systems both with and without H∞ performance and also designing an observer for state estimation and also as a controller.We show that through our proposed methodologies,a less conservative design procedure can be rendered for the filter and observer design.In particular,a so-called integrator method is proposed in this research work where an integrator is incorporated into the filter and observer structures.In doing so, the original systems can be transformed into augmented systems.Furthermore,the state-dependent function is selected in a way that its matrix is dependent only upon the original system state.Through this selection,a convex solution to the filter and observer design can be obtained efficiently.The existence of such filter and observer are given in terms of the solvability of polynomial matrix inequalities (PMIs).The problem is then formulated as sum of squares (SOS) constraints,therefore it can be solved by any SOS solvers.In this research work,SOSTOOLS is used as a SOS solver.Finally,to demonstrate the effectiveness and advantages of the proposed design methodologies in this thesis,numerical examples are given in filter design system.The simulation results show that the proposed design methodologies can estimate and stabilise the systems and achieve the prescribed performance requirements.