1 - 10 of 16 articles
Proper linear differential systems (whose coefficients are not necessarily bounded on the half-line) are defined as systems for which there exists a generalized Lyapunov transformation reducing them to a diagonal system with constant coefficients (Basov). We prove that Lyapunov’s original...
For a linear stationary system with skew-symmetric coefficient matrix, we construct formulas for the computation of its linear integrals. They permit one to describe the motion of a mechanical object on a sphere.
We show how to derive the differential equations of dynamic processes in various systems of units on the basis of extremal theory of dimensions and find out which of these systems are preferable for obtaining new theoretic results. We also obtain an unknown equation of motion in a gravitational...
For a mixed-type equation with the Lavrent’ev-Bitsadze operator, with a nonsmooth degeneration line, and with a delay in the derivative, we consider an analog of the Tricomi problem in a nonsymmetric domain.
We obtain an analog of the second Bogolyubov theorem for differential inclusions with multimappings acting in Sobolev spaces and satisfying some monotonicity and compactness conditions. As a consequence, we obtain criteria for the existence of periodic solutions of secondorder parabolic inclusions.
We construct a theory of realizations and controllability domains for linear stationary systems in the category of finitely generated free semimodules over a Boolean semiring. We show that the classical realization theorems cannot be generalized to this case, and we prove some incomplete analogs...
We study the limit behavior of the reachable set for singularly perturbed nonautonomous linear systems with geometric control constraints. We assume that the system is stable in the fast variables and its coefficients are Lipschitz functions of time. We obtain estimates for the convergence rate...
We consider the resource allocation problem for a two-sector economic model with a two-factor Cobb-Douglas production function on a finite time horizon with a terminal functional. The problem is reduced to some canonical form by a scaling of the phase variables and time. We prove the optimality...
We consider linear nonstationary hybrid differential-difference dynamical observable systems under the action of impulses, which generates jumps in the corresponding solutions of the systems. For such systems, we construct dual controllability problems and prove a general duality relation, which...
We consider optimal control problems for stationary systems whose solutions are unstable singular points of the corresponding evolution equations. We suggest a construction of a feedback control stabilizing the optimal state.
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