相关论文: Small-Gain Stability Analysis of Hyperbolic-Parabo…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
In this paper, we investigate the feedback stability of multiple-input multiple-output linear time-invariant systems with combined gain and phase information. To begin with, we explore the stability condition for a class of so-called easily…
We prove a small-gain theorem for interconnections of $n$ nonlinear heterogeneous input-to-state stable (ISS) control systems of a general nature, covering partial, delay and ordinary differential equations. Furthermore, for the same class…
We prove that under a small-gain condition, an interconnection of two globally incrementally exponentially stable systems inherits this property on any compact connected forward invariant set. It is also demonstrated that the…
We provide estimates for the asymptotic gains of the displacement of a vibrating string with endpoint forcing, modeled by the wave equation with Kelvin-Voigt and viscous damping and a boundary disturbance. Two asymptotic gains are studied:…
We propose a novel framework for stabilization, with an estimate of the region of attraction, of quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow-up phenomena when null boundary inputs are imposed.…
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…
We consider the problem of boundary feedback control of single-input-single-output (SISO) one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue of the output feedback stabilization is that it…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…
We derive conditions for the propagation of monotone ordering properties for a class of nonlinear parabolic partial differential equation (PDE) systems on metric graphs. For such systems, PDE equations with a general nonlinear dissipation…
Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a…
This paper systematically introduces dynamic extensions for the boundary control of general heterodirectional hyperbolic PDE systems. These extensions, which are well known in the finite-dimensional setting, constitute the dynamics of state…
In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov function in $ L^2- $norm is considered and discretised to…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
A better understanding of the instability margin will eventually optimize the operational range for safety-critical industries. In this paper, we investigate the almost-sure exponential asymptotic stability of the trivial solution of a…
For the stationary hydrodynamic model for semiconductors with sonic boundary, represented by Euler-Poisson equations, it possesses the various physical solutions including interior subsonic solutions/interior supersonic solutions/shock…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the…
This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…
We consider a nonlinear damped hyperbolic equation in $\real^n$, $1 \le n \le 4$, depending on a positive parameter $\epsilon$. If we set $\epsilon=0$, this equation reduces to the well-known Kolmogorov-Petrovski-Piskunov equation. We…