This paper develops a unified framework for studying robustness of the input-to-state stability (ISS) property and presents new results on robustness of ISS to slowly varying parameters, to rapidly varying signals, and to generalized singular perturbations. The common feature in these problems is a time-scale separation between slow and fast variables which permits the definition of a boundary ...

We consider a class of spatially distributed systems with spatially periodic coefficients. Frequency domain methods are used to convert a linear system belonging to this class into a family of infinite-dimensional LTI ones. The frequency and amplitude of the periodic coefficients are then treated as parameters. A perturbation analysis is then performed on the amplitude of the periodicity to fin...

This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustr...

This paper is devoted to the development of an optimal control system of trajectory movement of a mobile robot. Synthesis of the trajectory control law is based on the methods of optimal control and asymptotical methods of singular perturbation theory. Singular perturbation theory’s methods are used for reducing the order of the solving problem and it helps to simplify the realization of the co...

Sample rate conversion (SRC) with rational factors can be realized by interpolation followed by decimation, where CIC-Filters [1] can be chosen for either. However, the necessary increase of the sample rate that goes with the interpolation is not feasible in most RF-applications. Therefore a time-variant implementation of CIC-filters is presented which circumvents the high intermediate sample r...

In this Letter, we apply the homotopy-perturbation method (HPM) to obtain approximate analytical solutions of the time-dependent Emden– Fowler type equations. We also present a reliable new algorithm based on HPM to overcome the difficulty of the singular point at x = 0. The analysis is accompanied by some linear and nonlinear time-dependent singular initial value problems. The results prove th...

The article describes a method for approximately preserving the shape of discrete-time LTI system amplitude and phase responses while changing the frequency scale. The typical application cases include cutoff or sampling rate changes. Two versions of the method are presented, a simple and a topologypreserving one.