Partial Stability and Control

Investigating Stability with Respect to Part of the Variables in a Linear Approximation (2).- 2.5 Stability with Respect to Part of the Variables in a Nonlinear Approximation.- 2.6 Stability with Respect to Part of the Variables in Lyapunov Critical Cases.- 2.7 Overview of References.- 3 "Essentially" Nonlinear Problems of Stability with Respect to Part of the Variables.- 3.1 Using a New Class of Lyapunov Functions.- 3.2 Developing Theorems of the Barbashin-Krasovskii Type.- 3.3 Partial Stability in the Presence of Large Initial Perturbations.- 3.4 Using Differential Inequalities.- 3.5 Instability with Respect to Part of the Variables.- 3.6 Stability with Respect to a Specified Number of the Variables.- 3.7 Overview of References.- 4 Nonlinear Problems of Stabilization and Control with Respect to Part of the Variables.- 4.1 Stabilization with Respect to Part of the Variables.- 4.2 The Auxiliary Function of the Partial Stabilization Problem in Studying Problems of Stabilization with Respect to All the Variables and Polystabilization.- 4.3 Stabilization and Partial Stabilization of Permanent Rotations (of Equilibrium Positions) of a Solid and a Satellite in Orbit.- 4.4 Reorientation of an Asymmetric Solid and Coordinated Control of a System of Solids (Manipulator Model).- 4.5 Finite-Time Control with Respect to Part of the Variables with Constraints on Controls.- 4.6 The Nonlinear Problem of "Passage" of an Asymmetric Solid through a Given Angular Position.- 4.7 Overview of References.- 5 Nonlinear Game-Theoretic Problems of Control with Respect to Part of the Variablesunder Uncontrollable Interference.- 5.1 Guaranteed Conditions for Controllability with Respect to Part of the Variables under Uncontrollable Interference.- 5.2 The Nonlinear Game-Theoretic Problem of "Passage" of an Asymmetric Solid through a Given Angular Position.- 5.3 An Auxiliary Function of the Problem of Control with Respect to Part of the Variables in Game-Theoretic Problems of Control with Respect to All the Variables.- 5.4 The Nonlinear Game-Theoretic Problem of Triaxial Reorientation of an Asymmetric Solid (First Method of Solution).- 5.5 The Nonlinear Game-Theoretic Problem of Triaxial Reorientation of an Asymmetric Solid (Second Method of Solution).- 5.6 The Nonlinear Game-Theoretic Problem of Uniaxial Reorientation of an Asymmetric Solid.- 5.7 Overview of References.- 6 Stability and Stabilization of Functional-Differential Equations with Respect to Part of the Variables.- 6.1 Formulation of the Problem of Stability with Respect to Part of the Variables.- 6.2 Using the Method of Lyapunov-Krasovskii Functionals.- 6.3 Using the Method of Lyapunov Functions.- 6.4 The Stability of Linear Delayed Systems with Respect to Part of the Variables.- 6.5 The Stabilization of Linear Delayed Systems with Respect to Part of the Variables.- 6.6 The Stability of Nonlinear Delayed Systems in the Linear Approximation.- 6.7 Overview of References.- 7 Stability and Stabilization of Stochastic Systems with Respect to Part of the Variables.- 7.1 Formulation of the Problem of Stability with Respect to Part of the Variables.- 7.2 Using the Method of Lyapunov Functions.- 7.3 Damping of Rotational Motion of a Solid (with Respect to Part of the Variables) with Random Interference in Control Channels Taken into Account.- 7.4 The Stability of Linear Systems with Respect to Part ofthe Variables.- 7.5 Stability with Respect to Part of the Variables in a Linear Approximation.- 7.6 The Stabilization of Nonlinear Controlled Systems with Respect to Part of the Variables.- 7.7 Overview of References.- References.

"This monograph gives a detailed and comprehensive study of the stability and stabilisation of dynamical systems with respect to part of thevariables.... The monograph begins with an excellent Introduction. This places the topic of the monograph clearly in the historical development of the partial stability of dynamical systems, [and] includes a detailed account of the relevant literature and makes use of the monograph's comprehensive bibliography. Several situations are then described which help motivate and justify the need for a study of partial stability/stabilisation.

This is a well-written book. At well over 400 pages there is much to discover and digest. There are numerous useful examples, both of a textbook style, aimed to clarify a definition or detail in a proof, and those of a more significant application-based style. I found the applications to the control of geo-stationary orbit of satellites most interesting and illuminating. Each chapter is clearly introduced and each concludes with an extensive and impressive overview of the literature." -UK Nonlinear News