This paper focuses on the synthesis of well-conditioned rnultivariable robust controllers for a broad class of multi-input multi-output two-time-scale nonlinear systems with time-varying uncertain variables, modeled within the framework of singular perturbations. The proposed controller stabilizes the fast dynamics, guarantees boundedness of trajectories, and ensures that the ultimate discrepan...

Poisson-Nernst-Planck (PNP) systems are considered in the case of vanishing permanent charge. A detailed case study, based on natural categories described by system boundary conditions and flux, is carried out via simulation and singular perturbation analysis. Our results confirm the rich structure inherent in these systems. A natural quantity, the quotient of the Debye and characteristic lengt...

The stability of a nonlinear stochastic dynamic system with singular perturbations is considered. Based on the notion of stochastic input-to-state stability and using time scale decomposition, a result of the total stability type is obtained, i.e. if the fast subsystem and the slow subsystem are both input-to-state stable with respect to disturbances, then this property continues to hold for th...

abstract The singular value decomposition has a number of applications in digital signal processing. However, the the decomposition must be computed from a matrix consisting of both signal and noise. It is therefore important to be able to assess the eeects of the noise on the singular values and singular vectors | a problem in classical perturbation theory. In this paper we survey the perturba...

In this paper we consider the study of the servomechanism problem for multi-input multi-output (MIMO) linear time-invariant (LTI) positive systems. In particular, we present results on the tracking problem of nonnegative constant reference signals for unknown stable MIMO positive LTI systems with nonnegative constant disturbances. Our results exploit the structure of tuning regulators and show ...

We show how to optimize the shape of the transfer function of a linear time invariant (LTI) single-input-single-output (SISO) system. Since any transfer function is rational, this can be formulated as an optimization problem for the coefficients of polynomials. After characterizing the cone of polynomials which are nonnegative on intervals, we formulate this problem using semidefinite programmi...

We consider two periodically weighted model-matching problems with regard to a discrete-time LTI plant by means of discrete-time linear periodically time-varying (LPTV) control. These two problems are formulated by projection operators and shown to be determined uniquely by corresponding LTI model-matching problems in which new free parameters arise from the periodically time-varying property o...

We present a framework to synthesize lm 2 -stable control networks which are subject to delays and data dropouts. This framework can be applied to control systems which use “soft-real-time” cooperative schedulers and wired or wireless network feedback. The approach applies to passive plants and controllers that can be either linear, nonlinear, and (or) time-varying. This framework is based on f...

For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the normal form method, center manifold theory, and the renormalization group method are well known. It is shown that all of the solutions of the reduced equatio...