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We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
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…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
We develop a method to control discrete-time systems with constant but initially unknown parameters from linear temporal logic (LTL) specifications. We introduce the notions of (non-deterministic) parametric and adaptive transition systems…
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 study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This…
The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on \textit{collinear dynamical systems} and their variations are…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
Every irreducible discrete-time linear switching system possesses an invariant convex Lyapunov function (Barabanov norm), which provides a very refined analysis of trajectories. Until recently that notion remained rather theoretical apart…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
This paper provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…