Problems of stability and control with respect to part of variables (partial stability and control), including game-theoretical problems on partial control, naturally arise in applications and have been intensively in the second half of the 20th century. This book presents an efficient method of analysis and of control synthesis for problems on partial stability and control in dynamic systems. This method is based on efficient procedures of transformation of initial systems or their sub-systems (for controlled systems, together with a special choice of control structures) and facilitates essential simplification of solutions to problems. It is used to solve many linear and nonlinear problems, including non-linear game-theoretical problems which cannot be solved by standard methods, and it is also effective when applied in the first stages of solving problems on stability and control with respect to all variables. Space is given to non-linear game-theoretical problems retical problems of reorientation of an asymetric solid. Many examples (including computer simulations) considered in the book demonstrate the efficiency of the method.

Table of Contents:
0.1 Preliminary Remarks.- 0.2 General Situations and Specific Problems Leading to Investigation of Problems of Stability and Stabilization with Respect to Part of the Variables.- 0.3 Formulation of the Problems of Stability and Stabilization with Respect to Part of the Variables. Lines and Stages of Their Research.- 0.4 The Method of Lyapunov Functions in Problems of Stability and Stabilization with Respect to Part of the Variables.- 0.5 The Problem of Stability with Respect to Part of the Variables of Linear Systems, in Linear Approximation, and in Critical Cases.- 0.6 Special Features and Possibilities of the Problem of Stability with Respect to Part of the Variables.- 0.7 The Problem of Control with Respect to Part of the Variables in a Finite Time Interval.- 1 Linear Problems of Stability, Stabilization, and Control with Respect to Part of the Variables.- 1.1 Stability with Respect to Part of the Variables of Linear Systems with Constant Coefficients.- 1.2 Stability with Respect to Part of the Variables of Linear Systems with Periodic Coefficients.- 1.3 Stability with Respect to Part of the Variables of Linear Systems with Continuous Sufficiently Differentiable Coefficients.- 1.4 The Effect of Constantly Acting and Parametric Perturbations on Stability with Respect to Part of the Variables.- 1.5 Stabilization with Respect to Part of the Variables.- 1.6 Control with Respect to Part of the Variables.- 1.7 Overview of References.- 2 Nonlinear Problems of Stability with Respect to Part of the Variables in the First (Linear and Nonlinear) Approximation.- 2.1 Features of the Problem of Stability with Respect to Part of the Variables in a Linear Approximation.- 2.2 A Method of Nonlinear Transformation of Variables in Investigating Stability with Respect to Part of the Variables in a Linear Approximation (1).- 2.3 Damping (with Respect to Part of the Variables) of Angular Motions of an Asymmetric Solid.- 2.4 A Method of Nonlinear Transformation of the Variables in 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.