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Author: Michael I. Gil Publisher: Springer Science & Business Media ISBN: 9783540239840 Category : Technology & Engineering Languages : en Pages : 212
Book Description
Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.
Author: Michael I. Gil Publisher: Springer Science & Business Media ISBN: 9783540239840 Category : Technology & Engineering Languages : en Pages : 212
Book Description
Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.
Author: Michael I. Gil Publisher: Springer ISBN: 9783540805632 Category : Technology & Engineering Languages : en Pages : 190
Book Description
Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.
Author: Marcus Reble Publisher: Logos Verlag Berlin GmbH ISBN: 3832533818 Category : Mathematics Languages : en Pages : 159
Book Description
The objective of this thesis is the development of novel model predictive control (MPC) schemes for nonlinear continuous-time systems with and without time-delays in the states which guarantee asymptotic stability of the closed-loop. The most well-studied MPC approaches with guaranteed stability use a control Lyapunov function as terminal cost. Since the actual calculation of such a function can be difficult, it is desirable to replace this assumption by a less restrictive controllability assumption. For discrete-time systems, the latter assumption has been used in the literature for the stability analysis of so-called unconstrained MPC, i.e., MPC without terminal cost and terminal constraints. The contributions of this thesis are twofold. In the first part, we propose novel MPC schemes with guaranteed stability based on a controllability assumption, whereas we extend different MPC schemes with guaranteed stability to nonlinear time-delay systems in the second part. In the first part of this thesis, we derive explicit stability conditions on the prediction horizon as well as performance guarantees for unconstrained MPC. Starting from this result, we propose novel alternative MPC formulations based on combinations of the controllability assumption with terminal cost and terminal constraints. One of the main contributions is the development of a unifying MPC framework which allows to consider both MPC schemes with terminal cost and terminal constraints as well as unconstrained MPC as limit cases of our framework. In the second part of this thesis, we show that several MPC schemes with and without terminal constraints can be extended to nonlinear time-delay systems. Due to the infinite-dimensional nature of these systems, the problem is more involved and additional assumptions are required in the controller design. We investigate different MPC schemes with and without terminal constraints and/or terminal cost terms and derive novel stability conditions. Furthermore, we pay particular attention to the calculation of the involved control design parameters.
Author: Horst Leipholz Publisher: Springer Science & Business Media ISBN: 3642650732 Category : Technology & Engineering Languages : de Pages : 435
Book Description
Until recently there was no uniform stability theory. Different approaches to stability problems had been developed in the different branches of mechanics. In the field of elasticity, it was mainly the so called static method and energy method which were used, while in the field of dynamics it was the kinetic method, which found its perfect expression in the theory of Liapunov. During the last few decades there has been a rapid development in the general theory of stability, stimulated, for example, by the investigations of H. ZIEGLER on elastic systems subject to non-conservative loads, and by the problems arising in aeroelasticity which are closely related to those introduced by ZIEGLER. The need was felt for kinetic methods which could also be used in investigating the stability of deformable systems. Efforts were made to adapt such methods, already known and developed in the stability theory of rigid systems, for application in the stability theory of continuous systems. During the last ten years interest was focused mainly on the application of a generalized Liapunov method to stability problems of continuous systems. All this was done in attempts to unify the various approaches to stability theory. It was with the idea of encouraging such a tendency, establishing to what extent a uniform physical and mathematical foundation already existed for stability theory in all branches of mechanics, and stimulating the further deve lopment of a common stability theory, that a IUTAM-Symposium was devoted to this topic.
Author: Dmitry Altshuller Publisher: Springer ISBN: 1447142349 Category : Technology & Engineering Languages : en Pages : 142
Book Description
Frequency Domain Criteria for Absolute Stability focuses on recently-developed methods of delay-integral-quadratic constraints to provide criteria for absolute stability of nonlinear control systems. The known or assumed properties of the system are the basis from which stability criteria are developed. Through these methods, many classical results are naturally extended, particularly to time-periodic but also to nonstationary systems. Mathematical prerequisites including Lebesgue-Stieltjes measures and integration are first explained in an informal style with technically more difficult proofs presented in separate sections that can be omitted without loss of continuity. The results are presented in the frequency domain – the form in which they naturally tend to arise. In some cases, the frequency-domain criteria can be converted into computationally tractable linear matrix inequalities but in others, especially those with a certain geometric interpretation, inferences concerning stability can be made directly from the frequency-domain inequalities. The book is intended for applied mathematicians and control systems theorists. It can also be of considerable use to mathematically-minded engineers working with nonlinear systems.
Author: Leonid Berezansky Publisher: CRC Press ISBN: 1000048632 Category : Mathematics Languages : en Pages : 488
Book Description
Asymptotic properties of solutions such as stability/ instability,oscillation/ nonoscillation, existence of solutions with specific asymptotics, maximum principles present a classical part in the theory of higher order functional differential equations. The use of these equations in applications is one of the main reasons for the developments in this field. The control in the mechanical processes leads to mathematical models with second order delay differential equations. Stability and stabilization of second order delay equations are one of the main goals of this book. The book is based on the authors’ results in the last decade. Features: Stability, oscillatory and asymptotic properties of solutions are studied in correlation with each other. The first systematic description of stability methods based on the Bohl-Perron theorem. Simple and explicit exponential stability tests. In this book, various types of functional differential equations are considered: second and higher orders delay differential equations with measurable coefficients and delays, integro-differential equations, neutral equations, and operator equations. Oscillation/nonoscillation, existence of unbounded solutions, instability, special asymptotic behavior, positivity, exponential stability and stabilization of functional differential equations are studied. New methods for the study of exponential stability are proposed. Noted among them inlcude the W-transform (right regularization), a priory estimation of solutions, maximum principles, differential and integral inequalities, matrix inequality method, and reduction to a system of equations. The book can be used by applied mathematicians and as a basis for a course on stability of functional differential equations for graduate students.
Author: Publisher: Springer Science & Business Media ISBN: 0817644865 Category : Differentiable dynamical systems Languages : en Pages : 516
Book Description
In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.
Author: John Chiasson Publisher: Springer Science & Business Media ISBN: 354049555X Category : Technology & Engineering Languages : en Pages : 355
Book Description
This book provides an update of the latest research in control of time delay systems and applications by world leading experts. It will appeal to engineers, researchers and students in Control.
Author: He-Sheng Wang Publisher: Springer Science & Business Media ISBN: 9781846282898 Category : Technology & Engineering Languages : en Pages : 182
Book Description
The authors present a study of the H-infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. They derive necessary and sufficient conditions for the existence of a controller solving the standard nonlinear H-infinity control problem considering both state and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of Hamilton–Jacobi inequalities and a weak coupling condition; a parameterization of output feedback controllers solving the problem is also provided. All of these results are then specialized to the linear case. The derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. Among other important topics covered are balanced realization, reduced-order controller design and mixed H2/H-infinity control. "H-infinity Control for Nonlinear Descriptor Systems" provides a comprehensive introduction and easy access to advanced topics.
Author: Wudhichai Assawinchaichote Publisher: Springer ISBN: 3540370129 Category : Technology & Engineering Languages : en Pages : 180
Book Description
Most real physical systems are nonlinear in nature. Control and ?ltering of nonlinear systems are still open problems due to their complexity natures. These problem becomes more complex when the system’s parameters are - certain. A common approach to designing a controller/?lter for an uncertain nonlinear system is to linearize the system about an operating point, and uses linear control theory to design a controller/?lter. This approach is successful when the operating point of the system is restricted to a certain region. H- ever, when a wide range operation of the system is required, this method may fail. ThisbookpresentsnewnovelmethodologiesfordesigningrobustH fuzzy ? controllers and robustH fuzzy ?lters for a class of uncertain fuzzy systems ? (UFSs), uncertain fuzzy Markovian jump systems (UFMJSs), uncertain fuzzy singularly perturbed systems (UFSPSs) and uncertain fuzzy singularly p- turbed systems with Markovian jumps (UFSPS–MJs). These new meth- ologies provide a framework for designing robustH fuzzy controllers and ? robustH fuzzy ?lters for these classes of systems based on a Tagaki-Sugeno ? (TS) fuzzy model. Solutions to the design problems are presented in terms of linear matrix inequalities (LMIs). To investigate the design problems, we ?rst describe a class of uncertain nonlinear systems (UNSs), uncertain nonlinear Markovianjumpsystems(UNMJSs),uncertainnonlinearsingularlyperturbed systems(UNSPSs)anduncertainnonlinearsingularlyperturbedsystemswith Markovian jumps (UNSPS–MJs) by a TS fuzzy system with parametric - certainties and with/without Markovian jumps. Then, based on an LMI - proach, we develop a technique for designing robustH fuzzy controllers and ? robustH fuzzy ?lters such that a given prescribed performance index is ? guaranteed.
Author: Michael I. Gil
Author: Michael I. Gil
Author: Michael I. Gil
Author: Marcus Reble
Author: Horst Leipholz
Author: Dmitry Altshuller
Author: Leonid Berezansky
Author: 
Author: John Chiasson
Author: He-Sheng Wang
Author: Wudhichai Assawinchaichote