The reliability of polyhedral homotopy continuation methods for solving a polynomial system becomes increasingly important as the dimension of the polynomial system increases. High powers of the homotopy continuation parameter t and ill-conditioned Jacobian matrices encountered in tracing of homotopy paths affect the numerical stability. We present modified homotopy functions with a new homotop...

We analyze the well-posedness and stability properties of a parameter dependent problem that models the reflection and transmission of electromagnetic waves at a thin and rapidly oscillating interface. The latter is modeled using approximate interface conditions that can be derived using asymptotic expansion of the exact solution with respect to the small parameter (proportional to the periodic...

Stability limits place restrictions on the available transfer capability (ATC) of power systems. Calculation of these limits is therefore very important, but has traditionally been quite difficult. This paper proposes an iterative algorithm for determining parameter values which result in marginal stability of a system. (A system is marginally stable for a particular disturbance if the postdist...

This paper presents the synchronization of chaotic systems subject to parameter uncertainties. Based on the fuzzy models of chaotic systems, a fuzzy controller is designed to realize chaotic synchronization. A design criterion of the membership functions of fuzzy controller is proposed to facilitate the stability design towards chaotic synchronization when parameter uncertainties are under cons...

Power system stability is quantified as the ability to regain an equilibrium state after being subjected to perturbations. We start by investigating the global basin stability of a single machine bus-bar system and then extend it to two and four oscillators. We calculate the basin stability of the stable fixed point over the whole parameter space, in which different parameter combinations give ...

This paper provides a class of feedback controllers that guarantee global stability of quantum angular momentum systems. The systems are in general finite dimensions and the stability is around an assigned eigenstate of observables with a specific form. It is realized by employing the control law which was proposed by Mirrahimi & van Handel. The class of stabilizing controllers is parameterized...

In this paper, we develop data-based methods to analyze the characteristics of linear discrete-time systems, which have unknown parameter matrices. These characteristics include output controllability, asymptotic stability of the equilibrium point, bounded-input boundedstate stability, and bounded-input bounded-output stability. Our methods only use measured state and output data to verify the ...

Abstract: This paper presents a new procedure for discrete-time robust structured control design. Parameter-dependent nonconvex conditions for stabilizable and induced L2-norm performance controllers are solved by an iterative linear matrix inequalities (LMI) optimization. A wide class of controller structures including decentralized of any order, fixed-order dynamic output feedback, static out...

The problem of boundary control in first order linear parameter varying (LPV) hyperbolic systems with dynamics associated with the boundary conditions is considered in this article. By means of Lyapunov based techniques, some sufficient conditions are derived for the exponential stability of these infinite dimensional systems. A polytopic approach is developed in order to synthesize a robust bo...

Using the cavity method I derive the microscopic equations and their stability condition for learning in neural networks. Iterating the microscopic equations provides a general algorithm for learning. Macroscopic results agree with the replica theory and the Almeida-Thouless stability condition. They are applied to derive the evolution equations of the overlap order parameter and the noise para...