Related papers: Oscillation criteria for extended linear matrix Ha…
Contraction properties of the Riccati operator are studied within the context of non-stationary linear-quadratic optimal control. A lifting approach is used to obtain a bound on the rate of strict contraction, with respect to the Riemannian…
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
We consider matrix Riccati inequality arising in the theory of absolute stability, $H_\infty$ control problem, $LQ$ problem, and optimal estimation problem. In the case of sign definite frequency domain function, the solvability of Riccati…
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…
The dynamical law obeyed by the one-dimensional physical systems in the scale relativity approach is reduced to a Riccati nonlinear differential equation. Applied to the harmonic oscillator potential, we show that such an approach permits…
A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
Some global existence criteria for quaternionic Riccati equations are established. Two of them are used to prove a completely non conjugation theorem for solutions of linear systems of ordinary differential equations.
Many recent works on stabilization of nonlinear systems target the case of locally stabilizing an unstable steady state solutions against small perturbation. In this work we explicitly address the goal of driving a system into a…
This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic…
In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…
The Riccati inequality and equality are studied for infinite dimensional linear discrete time stationary systems with respect to the scattering supply rate. The results obtained are an addition to and based on our earlier work on the…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…
We provide sufficient criteria for the oscillation of all solutions of neutral delay differential equations of the form \[ \left[x(t) - \sum_{i=1}^{N_r}R_i(t)x(t - r_i(t)) \right]' + \sum_{i=1}^{N_p}P_i(t)x(t - \tau_i(t)) -…