The estimation of Linear Time Invariant (LTI) models is a standard procedure in System Identification. Any real-life system will however be nonlinear and time-varying, and the estimated model will converge to the LTI second order equivalent (LTI-SOE) of the true system. In this paper we consider some aspects of this convergence and the distance between the true system and its LTI-SOE. We show t...

This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An expl...

We consider a class of stochastic differential equations in singular perturbation form, where the drift terms are linear and diffusion terms are nonlinear functions of the state variables. In our previous work, we approximated the slow variable dynamics of the original system by a reduced-order model when the singular perturbation parameter is small. In this work, we obtain an approximation for...

Most of control systems in vogue are Linear Time Invariant (LTI) systems and are characterized by several parameters such as settling time, over shoot and rise time etc. Optimization of these parameters is required to meet the desired system response and smooth operation of the system. In this paper, an optimization based compensator is designed and implemented for a closed loop LTI system and ...

in chemical engineering, several processes are represented by singular boundary value problems. in general, classical numerical methods fail to produce good approximations for the singular boundary value problems. in this paper, chebyshev finite difference (chfd) method and dtm-pad´e method, which is a combination of differential transform method (dtm) and pad´e approximant, are applied for sol...

The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost) periodic vector fields are considered. Theorems on error estimates for approximate solutions, existence of approximate invariant manifolds and their stability, i...

We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

A singular perturbation problem from the artificial compressible system to incompressible is considered for a doubly diffusive convection when Hopf bifurcation motionless state occurs in system. It proved that also small parameter, called Mach number. The time periodic solution branch of shown converge corresponding bifurcating limit vanishing

We consider the problem of robust stability for uncertain systems described in terms of multiple scalar structured time-invariant perturbations, which are norm bounded. The issue we address is the role that the type of perturbation norm plays in the robust stability conditions. To this end, the L p-induced norms (for 1 p 1) on the perturbations are considered, and some simple relations between ...