Mathematical Methods for the Study of Automatic Control Systems |
Contents
PREFACE TO THE RUSSIAN EDITION | 1 |
Chapter II | 70 |
New method of constructing the regions of stability in the space | 115 |
Copyright | |
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Common terms and phrases
approximation asymptotically stable automatic control system b₁ based on system c₁ characteristic values coefficients conditions of Theorem consider the system constantly acting perturbations construction continuous functions continuously differentiable convergence correlation functions curves of system defined denote differential equations dv dt dy's dt equations dx exists a number follows formula function V(y1 given h₁ homogeneous solution infinitely small upper initial conditions integral curve linear system Lyapunov function matrix members of system method necessary and sufficient negative-definite nonlinear obtain parameters periodic solution polynomials positive constants positive-definite positive-definite function problem of stability PROOF quadratic form quantities region right-hand members roots satisfies the inequalities satisfying the conditions self-oscillation small upper bound solution of system stochastic process sufficiently small system of differential system of equations system of solutions t₁ total derivative transient processes trigonometric polynomials V₁ variable W₁ x₁ y₁ zero Φι