Front Cover; Analysis and Synthesis of Polynomial Discrete-Time Systems; Copyright; Contents; About the Authors; Preface; 1 Introduction; 1.1 Nonlinear systems; 1.2 Nonlinear discrete-time systems; 1.2.1 Discretization; 1.2.2 Brief overview on the literature of nonlinear discrete-time systems; 1.3 Polynomial systems; 1.3.1 Recent work on polynomial systems; 1.3.1.1 On the literature on controller synthesis for polynomial systems: the Lyapunov method and SOS decomposition approach; 1.3.2 Sum-of-squares (SOS) decomposition; 1.3.2.1 SOSTOOLS; 1.4 Research motivation; 1.5 Contribution of the book.
1.6 Book outline References; 2 Robust nonlinear control for polynomial discrete-time systems; 2.1 Introduction; 2.2 Main results; 2.2.1 Nonlinear control for polynomial discrete-time systems; 2.2.1.1 The integrator approach; 2.2.2 Robust nonlinear feedback control design for polynomial discrete-time systems; With parametric uncertainties; With norm-bounded uncertainties; 2.3 Numerical examples; 2.4 Conclusion; References; 3 Robust nonlinear H8 state feedback control for polynomial discrete-time systems; 3.1 Introduction; 3.2 System description and problem formulation.
3.2.1 System description3.2.2 Problem formulation; 3.3 Main results; 3.3.1 Nonlinear H8 control of polynomial discrete systems; 3.3.2 Robust nonlinear H8 control of polynomial discrete systems; 3.3.2.1 Parametric uncertainty; 3.3.2.2 Norm-bounded uncertainties; 3.4 Numerical examples; References; 4 Robust nonlinear ltering for polynomial discrete-time systems; 4.1 Introduction; 4.2 System description and de nition; 4.3 Main results; 4.3.1 Nonlinear ltering for polynomial discrete-time systems; 4.3.2 Robust nonlinear ltering for polynomial discrete-time systems; 4.4 Numerical examples.
4.5 Conclusion References; 5 Robust nonlinear H8 ltering for polynomial discrete-time systems; 5.1 Introduction; 5.2 System description and problem formulation; 5.3 Main results; 5.3.1 Nonlinear H8 ltering for polynomial discrete-time systems; 5.3.2 Robust nonlinear H8 ltering for polynomial discrete-time systems; 5.4 Numerical examples; 5.5 Conclusion; References; 6 Robust nonlinear H8 output feedback control for polynomial discrete-time systems; 6.1 Introduction; 6.2 System description and problem formulation; 6.3 Main results; 6.3.1 Nonlinear H8 output feedback control.
6.3.2 Robust nonlinear H8 output feedback control6.3.2.1 Parametric uncertainties; 6.3.2.2 Norm-bounded uncertainties; 6.4 Numerical examples; 6.5 Conclusion; References; 7 Global stabilization of fuzzy polynomial discrete-time nonlinear systems; 7.1 Introduction; 7.2 System description and problem formulation; 7.3 Main results; 7.4 Simulation examples; 7.5 Conclusion; References; 8 Global H8 control of fuzzy polynomial discrete-time nonlinear systems; 8.1 Introduction; 8.2 System description and preliminaries; 8.3 Main results; 8.4 Simulation examples; 8.5 Conclusion; References.
Summary
Analysis and Synthesis of Polynomial Discrete-time Systems: An SOS Approach addresses the analysis and design of polynomial discrete-time control systems. The book deals with the application of Sum of Squares techniques in solving specific control and filtering problems that can be useful to solve advanced control problems, both on the theoretical side and on the practical side. Two types of controllers, state feedback controller and output feedback controller, along with topics surrounding the nonlinear filter and the H-infinity performance criteria are explored. The book also proposes a solution to global stabilization of discrete-time systems.
