Related papers: Flatness of Two-Input Discrete-Time Systems and th…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not extend to their sampled counterparts, i.e., for a given…
We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the…
This paper proposes a tracking controller based on the concept of flat inputs and a dynamic compensator. Flat inputs represent a dual approach to flat outputs. In contrast to conventional flatness-based control design, the regulated output…
Linear observed systems on manifolds are a special class of nonlinear systems whose state spaces are smooth manifolds but possess properties similar to linear systems. Such properties can be characterized by preintegration and exact…
We introduce a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs, with $N\times N$ matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs and the associated discrete integrable systems. We present…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the…
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…
This chapter presents an approach to embed the input/state/output constraints in a unified manner into the trajectory design for differentially flat systems. To that purpose, we specialize the flat outputs (or the reference trajectories) as…
Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…
This paper addresses the problem of stabilization for infinite-dimensional systems. In particular, we design nonlinear stabilizers for both linear and nonlinear abstract systems. We focus on two classes of systems: the first class comprises…
This paper examines a broadly applicable triangular normal form for x-flat control-affine systems with two inputs. First, we show that this triangular form encompasses a wide range of established normal forms. Next, we prove that any x-flat…
Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat…
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…
Continuous time (CT) and discrete time (DT) linear time invariant (LTI) systems are commonly introduced through distinct mathematical formalisms, which can obscure their underlying dynamical equivalence. This tutorial presents a unified…
Let's consider a control system described by the implicit equation $F(x,\dot x) = 0$. If this system is differentially flat, then the following criterion is satisfied : For some integer $r$, there exists a function $\varphi(y_0, y_1,…
We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a…
This paper studies the $\alpha$-stability property of differentially flat nonlinear dynamical systems. The results build off the recently introduced notion of $\alpha$-stability, which is particularly amenable to characterize the ability of…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…