Related papers: Stability of switched linear hyperbolic systems by…
In this paper, we investigate the robustness to external disturbances of switched discrete and continuous systems with multiple equilibria. It is shown that if each subsystem of the switched system is Input-to-State Stable (ISS), then under…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
This paper proposes a backstepping boundary control design for robust stabilization of linear first-order coupled hyperbolic partial differential equations (PDEs) with Markov-jumping parameters. The PDE system consists of 4 X 4 coupled…
In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established the necessary and sufficient condition for the asymptotic…
This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…
Asymptotic hyperstability is achievable under certain switching laws if at least one of the feed-forward parameterization: 1) possesses a strictly positive real transfer function, 2) a minimum residence time interval is respected for each…
We develop an input delay-compensating feedback law for linear switched systems with time-dependent switching. Because the future values of the switching signal, which are needed for constructing an exact predictor-feedback law, may be…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
For switched systems that switch between distinct globally stable equilibria, we offer closed-form formulas that lock oscillations in the required neighborhood of the equilibria. Motivated by non-spiking neuron models, the main focus of the…
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…
In this work, we propose a methodology for the expression of necessary and sufficient Lyapunov-like conditions for the existence of stabilizing feedback laws. The methodology is an extension of the well-known Control Lyapunov Function (CLF)…
Selected results for the stability and optimal control of abstract switched systems in Banach and Hilbert space are reviewed. The dynamics are typically given in a piecewise sense by a family of nonlinearly perturbed evolutions of strongly…
In hyperbolic dynamics, a well-known result is: every hyperbolic Lyapunov stable set, is attracting; it's natural to wonder if this result is maintained in the sectional-hyperbolic dynamics. This question is still open, although some…
This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
This paper studies the problem of stabilizing a continuous-time switched linear system by quantized output feedback. We assume that the quantized outputs and the switching signal are available to the controller at all time. We develop an…
The key challenges in design of predictor-based control laws for switched systems with arbitrary switching and long input delay are the potential unavailability of the future values of the switching signal (at current time) and the fact…
Starting from a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations is a Lyapunov function, establishing stability for two kinds of nonlinear…