Related papers: Improved finite-time stability and instability the…
Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing…
Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result…
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…
In this work, we propose the design and analysis of a novel continuous robust controller for a class of multi--input multi--output (MIMO) nonlinear uncertain systems. The systems under consideration contains unstructured uncertainties in…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite…
We study stability issue of reset and impulsive switched systems. We find time constraints (dwell time and flee time) on switching signals which stabilize a given reset switched system. For a given collection of matrices, we find an…
Motivated by the regulator theory and adaptive controls, several notions on output stability in the framework of input-to-state stability (iss) were introduced for finite-dimensional systems. It turned out that these output stability…
This work is devoted to investigate the stability properties of time-delay reset systems. We present a Lyapunov-Krasovskii proposition, which generalizes the available results in the literature, providing results for verifying the stability…
This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the…
In this paper we show that the existence of a Lyapunov-Krasovskii functional is necessary and sufficient condition for the uniform global asymptotic stability and the global exponential stability of time-invariant systems described by…
We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…
We develop a Lyapunov-based small-gain theorem for establishing fixed-time input-to-state stability (FxT-ISS) guarantees in interconnected nonlinear dynamical systems. The proposed framework considers interconnections in which each…
This paper presents a novel scalable framework to solve the optimization of a nonlinear system with differential algebraic equation (DAE) constraints that enforce the asymptotic stability of the underlying dynamic model with respect to…
Many physical systems are inherently time-varying in nature. When these systems are linearized around a trajectory, generally, the resulting system is Linear Time-Varying (LTV). LTV systems describe an important class of linear systems and…
In this paper, we present Lyapunov-based robust and adaptive controllers for the finite time stabilization of a perturbed chain of integrators with bounded uncertainties. The proposed controllers can be designed for integrator chains of any…
For stochastic systems with nonvanishing noise, i.e., at the desired state the noise port does not vanish, it is impossible to achieve the global stability of the desired state in the sense of probability. This bad property also leads to…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…