We study the stability characteristic of the active disturbance rejection control for a nonlinear, time-varying plant. To this end, the closed-loop system is reformulated in a form that allows the singular perturbation method to be applied. Since singular perturbation approach enables the decomposition of the original system into a relatively slow subsystem and a relatively fast subsystem, the ...

We consider the 2-norm distance τr(A,B) from a linear time-invariant dynamical system (A,B) of order n to the nearest system (A + ∆A∗, B + ∆B∗) whose reachable subspace is of dimension r < n. We first present a characterization to test whether the reachable subspace of the system has dimension r, which resembles and can be considered as a generalization of the Popov-Belevitch-Hautus test for co...

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. W...

The direct applicability of SVD-based methods in model reduction of large linear systems is very limited. However, substructuring methods are a possibility to use these approaches. A method called Automated Multilevel Substructuring (AMLS) has been successfully applied to eigenvalue computations of very large systems. We present a similar substructuring approach for linear time-invariant (LTI) ...

We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for traveling wave solutions of a free boundary problem obtained as singular limit for the reaction-diffusion equation (the so-called high energy activation energy l...

We consider the asymptotic analysis and some existence result on blowing up solutions for a semilinear elliptic equation in dimension 2 with nonlinear exponential term, singular sources and Dirichlet boundary condition.

Assume that the reproduction rate ratio zeta of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit zeta=0, a singular Shilnikov's saddle-focus homocli...