Most dynamic models of interest in machine learning, robotics, AI or cognitive science are nonautonomous and input-driven. In the last few years number of important innovations have occurred in mathematical research on nonautonomous systems. In understanding the long term behavior of nonautonomous systems, the notion of an attractor is fundamental. With a time varying input, it turns out that f...

In the paper, the bang-bang principle for a control system connected with a system of linear nonautonomous partial differential equations of hyperbolic type (the socalled Goursat-Darboux problem or continuous Fornasini-Marchesini problem) is proved. Some density result is also obtained.

A nonautonomous system of ordinary differential equations is considered. This system has the zero solution, and there exists a nonnegative Lyapunov function which derivative is nonpositive. Theorems of the partial uniform stability and partial uniform asymptotic stability are proved. Copyright c ©2005 IFAC

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...

In the present paper, sufficient conditions are obtained under which Cauchy problem for a nonlinearly perturbed nonautonomous neutral fractional system with distributed delays and Caputo type derivatives has unique solution in case of initial functions first-kind discontinuities. For this system, by applying formula integral presentation nonhomogeneous linear we found some additional natural to...

In 1 , the general nonautonomous n-species Lotka-Volterra competitive systems with impulsive effects are investigated. By using the methods of inequalities estimate and constructing the suitable Liapunov functions, the sufficient conditions on the permanence of whole species and global attractivity of systems are established. In 2 , the authors studied the following general nonautonomous n-spec...

This paper concerns the square-mean almost periodic solutions to a class of nonautonomous stochastic differential equations on a separable real Hilbert space. Using the so-called ‘Acquistapace-Terreni’ conditions, we establish the existence and uniqueness of a square-mean almost periodic mild solution to those nonautonomous stochastic differential equations.