Finite-Time Stability: An Input-Output Approach

FRANCESCO AMATO is Professor of Bioengineering, Dean of the School of Computer and Biomedical Engineering and the Coordinator of the Doctorate School in Biomedical and Computer Engineering at the University of Catanzaro, Italy. The scientific activity of Francesco Amato has developed in the fields of systems and control theory; robust control, finite-time stability and control, control of nonlinear quadratic systems with applications to the contexts of aircraft control, computational biology and bioengineering. He has published around 250 papers in international journals and conference proceedings and two monographs with Springer Verlag entitled "Robust Control of Linear Systems subject to Uncertain Time-Varying Parameters" and "Finite-Time Stability and Control". GIANMARIA DE TOMMASI is Associate Professor with the Department of Electrical Engineering and Information Technology, University of Naples Federico II, Italy. Since 2002, he has been a Visiting Researcher with the Joint European Torus (JET) Tokamak, Oxfordshire, U.K., where he has participated in various projects connected to the JET plasma current and shape control system. He has authored more than 100 journal and conference papers, and is a co-author of the monograph "Finite-Time Stability and Control" (Springer). His current research interests include control of nuclear fusion devices, fault detection for discrete event systems, identification of discrete event systems modeled with Petri nets, and stability on finite-time horizon of hybrid systems. Dr. De Tommasi is a member of the IEEE Control System Society Conference Editorial Board, and has been Guest Editor of the Fusion Engineering and Design special issue titled "Design and Implementation of Real-Time Systems for Magnetic Confined Fusion Devices". ALFREDO PIRONTI is a Full Professor of System and Control Theory in the Department of Electrical and Information Technology Engineering, University of Naples Federico II, Italy. He spent several periods as visiting researcher at the Max Planck Institute for Plasma Physics in Garching (Germany), the Center for Control Engineering and Computation (University of California at Santa Barbara), the ITER Joint Work Site of Naka (Japan), and the EFDA-JET site of Culham (UK). His research interests include application of feedback control to nuclear fusion problems, robust control of uncertain systems, and differential games theory. In 2005 he was guest editor for the IEEE Control Systems Magazine journal, where he contributed to two special issues focused on the control of plasmas in tokamak machines. He is the author of more than 200 papers published in international journals, books, and conference proceedings.

• Preface xiList of Acronyms xiii1. Introduction 11.1 Finite-Time Stability (FTS) 11.2 Input-Output Finite-Time Stability 61.3 FTS and Finite-Time Convergence 101.4 Background 101.4.1 Vectors and signals 101.4.2 Impulsive dynamical linear systems 121.5 Book Organization 132. Linear Time-Varying Systems: IO-FTS Analysis 152.1 Problem Statement 152.2 IO-FTS for W2 Exogenous Inputs 162.2.1 Preliminaries 162.2.2 Necessary and sufficient conditions for IO-FTS for W2 exogenous inputs 222.2.3 Computational issues 252.3 A Sufficient Condition for IO-FTS for W∞ Inputs 262.4 Summary 293. Linear Time-Varying Systems: Design of IO Finite-Time Stabilizing Controllers 333.1 IO Finite-Time Stabilization via State Feedback 343.2 IO-Finite-Time Stabilization via Output Feedback 363.3 Summary 424. IO-FTS with Nonzero Initial Conditions 454.1 Preliminaries 454.2 Interpretation of the Norm of the Operator LSNZ 484.3 Sufficient Conditions for IO-FTS-NZIC 524.4 Design of IO Finite-Time Stabilizing Controllers NZIC 554.4.1 State feedback 564.4.2 Output feedback 574.5 Summary 585. IO-FTS with Constrained Control Inputs 615.1 Structured IO-FTS and Problem Statement 615.2 Structured IO-FTS Analysis 635.3 State Feedback Design 655.4 Design of an Active Suspension Control System Using Structured IO-FTS 675.5 Summary 706. Robustness Issues and the Mixed H∞/FTS Control Problem 716.1 Preliminaries 726.1.1 System setting 726.1.2 IO-FTS with an H∞ bound 736.2 Robust and Quadratic IO-FTS with an H∞ Bound 776.2.1 Main result 786.2.2 A numerical example 806.3 State Feedback Design 826.3.1 Numerical example: Cont’d 856.4 Case study: Quadratic IO-FTS with an H∞ Bound of the Inverted Pendulum 866.5 Summary 887. Impulsive Dynamical Linear Systems: IO-FTS Analysis 897.1 Background 907.1.1 Preliminary results for the W2 case 907.2 Main Results: Necessary and Sufficient Conditions for IO-FTS in Presence of W2 Signals 917.3 Example and Computational Issues 967.4 Main Result: A Sufficient Condition for IO-FTS in Presence of W∞ Signals 987.4.1 An illustrative example 997.5 Summary 1008. Impulsive Dynamical Linear Systems: IO Finite-Time Stabilization via Dynamical Controllers 1038.1 Problem Statement 1038.2 IO Finite-Time Stabilization of IDLSs: W2 Signals 1048.2.1 A numerical example 1078.3 IO Finite-Time Stabilization of IDLSs: W∞ Signals 1088.3.1 Illustrative example: Cont’d 1108.4 Summary 1119. Impulsive Dynamical Linear Systems with Uncertain Resetting Times 1139.1 Arbitrary Switching 1139.2 Uncertain Switching 1149.3 Numerical Example 1169.3.1 Known resetting times 1179.3.2 Arbitrary switching 1189.3.3 Uncertain switching 1189.4 Summary 11910. Hybrid Architecture for Deployment of Finite-Time Control Systems 12110.1 Controller Architecture 12110.2 Examples 12310.2.1 Hybrid active suspension control 12310.2.2 Lateral collision avoidance system 12410.3 Summary 129A. Fundamentals on Linear Time-Varying Systems 131B. Schur Complements 137C. Computation of Feasible Solutions to Optimizations ProblemsInvolving DLMIs 139 D. Solving Optimization Problems Involving DLMIs using MATLAB® 145E. Examples of Applications of IO-FTS Control Design to Real-World Systems 151References 159Index 167