Related papers: Uniform Detectability of Linear Time Varying Syste…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and…
We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…
Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many such problems, the dominant…
For nonautonomous linear difference equations in Banach spaces we show that a very general type of dichotomic behavior persists under small enough additive linear perturbations. By using a new approach, we obtain two general robustness…
For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach…
The property of exponential dichotomy can be seen as a generalization of the hyperbolicity condition for non autonomous linear finite dimensional systems of ordinary differential equations. In 1978 W.A. Coppel proved that the exponential…
An observability problem for linear autonomous distributed systems in the class of linear operations is considered. A criterion of observability with respect to terminal state has been proved. A connection with observability with respect to…
Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the…
We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires i) exponential decay in time of the space-derivatives of the semigroup…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
This paper is devoted to discuss the stabilizability of a class of $ 2 \times2 $ non-homogeneous hyperbolic systems. Motivated by the example in \cite[Page 197]{CB2016}, we analyze the influence of the interval length $L$ on stabilizability…
In many sampled-data applications, observers are designed based on approximately discretized models of continuous-time systems, where usually only the discretized system is analyzed in terms of its detectability. In this paper, we show that…
This paper introduces a Distributed Unknown Input Observer (D-UIO) design methodology that uses a technique called node-wise detectability decomposition to estimate the state of a discrete-time linear time-invariant (LTI) system in a…
We prove that small nonlinear perturbations of random linear dynamics admitting a tempered exponential dichotomy have a random version of the shadowing property. As a consequence, if the exponential dichotomy is uniform, we get that the…
Exponentially stable extended adaptive observer is proposed for a class of linear time-invariant systems with unknown parameters and overparameterization. It allows one to reconstruct unmeasured states and bounded external disturbance…
In this paper, we develop a novel contraction framework for stability analysis of discrete-time nonlinear systems with parameters following stochastic processes. For general stochastic processes, we first provide a sufficient condition for…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…