This paper presents a singular perturbation stability analysis for a nonlinear three-time-scale autonomous helicopter model in vertical flight. The presented time-scale analysis permits to conduct a stability analysis for the singular perturbed threetime-scale system, and allows to construct a composite Lyapunov function for the resultant closed-loop system using time-scale separation. The meth...

The robust servomechanism problem consists in finding an LTI controller for the plant so that: (i) the resultant closed-loop system is asymptotically stable, (ii) asymptotic tracking occurs, and (iii) condition (ii) holds any arbitrary perturbation in the plant model (parametric uncertainty or dynamic uncertainty, including changes in model order) that do not cause the resultant closed-loop sys...

We treat the problem of robustness of output feedback controllers with respect to singular perturbations. Given a singularly perturbed control system whose boundary layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a (possibly dynamical) output feedback controller, we present a sufficient condition which ensures that the system obtained by app...

This paper concerned with a model reduction of infinite dimensional systems by using the singular perturbation approximation. The system considered is that of the exponentially stable linear system with bounded and finite-rank input and output operators such that the balanced realization can be performed on the system. Furthermore, the singular perturbation method is applied to reduce the order...

In this paper, the problem of bifurcation of limit cycles from degenerate singular point and infinity in a class of septic polynomial differential systems is investigated. Using the computer algebra system Mathematica, the limit cycle configurations of {(8), 3} and {(3), 6} are obtained under synchronous perturbation at degenerate singular point and infinity. To our knowledge, up to now, this i...

A new approach for pole placement of nonlinear systems using state feedback and fuzzy system is proposed. We use a new online fuzzy training method to identify and to obtain a fuzzy model for the unknown nonlinear system using only the system input and output. Then, we linearized this identified model at each sampling time to have an approximate linear time varying system. In order to stabilize...

It has recently been shown that a necessary and sufficient condition for the μstabilization of a linear time-invariant (LTI) retarded time-delay system by LTI decentralized finite-dimensional controllers is that the system should not have any μ-decentralized fixed modes with respect to decentralized static feedback. In the present work, we consider the stabilization of such systems by decentral...

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 investigates sufficient conditions to obtain harmonic oscillation for high-order LTI systems. The paper presents a design procedure for controlling harmonic ...