Md Saat, Mohd Shakir
(2012)
*CONTROLLER SYNTHESIS FOR POLYNOMIAL DISCRETE-TIME SYSTEMS.*
PhD thesis, The University of Auckland.

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## Abstract

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 controller design for polynomial discrete-time systems. The main reason for focusing on this area is because the controller 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 controller matrix is not jointly convex when the parameter-dependent or state-dependent Lyapunov function is under consideration. Therefore the problem cannot possibly be solved via semidenite programming (SDP). In light of the aforementioned problem, weestablish novel methodologies of designing controllers for stabilising the systems both with and without H-infinity performance and for the systems with and without uncertainty. Two types of uncertainty are considered in this research work; 1. Polytopic uncertainty, and 2. Norm-bounded uncertainty. A novel methodology for designing a filter for the polynomial discrete-time systems is also developed. We show that through our proposed methodologies, a less conservative design procedure can be rendered for the controller synthesis and filter design. In particular, a so-called integrator method is proposed in this research work where an integrator is incorporated into the controller and filter structures. In doing so, the original systems can be transformed into augmented systems. Furthermore, the state-dependent Lyapunov 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 controller design and the filter design can be obtained eciently. However, the price we pay for incorporating the integrator into the controller and filter structures is a large computational cost, which prevents us from using this method in general. To reduce the computational requirements for our design methodologies a number of simpler classes of polynomial systems are considered. Based on this integrator approach, we first consider the state feedback control problem. In this case, the nonlinear state feedback control is tackled first and followed by the robust control problem in which the uncertain terms are described as polytopic forms. The robust control problem with norm-bounded uncertainty is studied next. Then, we discuss the nonlinear H-infinity state feedback control problem and robust nonlinear h-infinity state-feedback control problem with polytopic and norm-bounded uncertainty. The design ensures that the ratio of the regulated output energy and the disturbance energy is less than a prescribed performance level. The filter design is tackled next and followed by the output feedback control problem. In the output feedback control, the problem of system uncertainties and disturbances are addressed. The existence of such controllers and a filter 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 each designed control system. The simulation results show that the proposed design methodologies can stabilise the systems and achieve the prescribed performance requirement.

Item Type: | Thesis (PhD) |
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Subjects: | T Technology > TK Electrical engineering. Electronics Nuclear engineering |

Divisions: | Faculty of Electronics and Computer Engineering > Department of Industrial Electronics |

Depositing User: | DR. Mohd Shakir Md Saat |

Date Deposited: | 31 Jul 2013 04:27 |

Last Modified: | 28 May 2015 03:54 |

URI: | http://eprints.utem.edu.my/id/eprint/8214 |

Statistic Details: | View Download Statistic |

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