Related papers: A Flat System Possessing no (x,u)-Flat Output
We consider flat differential control systems for which there exist flat outputs that are part of the state variables and study them using Jacobi bound. We introduce a notion of saddle Jacobi bound for an ordinary differential system of $n$…
Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\alpha(t)$ takes values in $[0,1]$ and is persistently exciting, i.e., there exist two positive constants $\mu,T$ such that, for every…
The suggestion of writing, for some problems, nonlinear state equations not as dx/dt = F(x,u,t), but as dx/dt = [A(t,x)]x + [B(t,x)]u(t), which is more "constructive", is considered supported by arguments related to: the axiomatization of…
This paper is devoted to normal forms for x-flat control-affine systems with two inputs. We propose a general triangular normal form which contains several other normal forms discussed in the literature as special cases. We derive…
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…
Despite ongoing research, testing the flatness of discrete-time systems remains a challenging problem. To date, only the property of forward-flatness - a special case of difference-flatness - can be checked in a computationally efficient…
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 propose an algorithmic test to check whether a two-input system is linearizable by an endogenous dynamic feedback with a dimension of at most two. This test furthermore provides a procedure for systematically deriving flat outputs for…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
We introduce a task-relative taxonomy of actuator inputs for nonlinear systems within the input-output feedback-linearization framework. Given a flat output specifying the task, inputs are classified as essential, redundant, or dexterity:…
This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each…
Recently it has been shown that the property of forward-flatness for discrete-time systems, which is a generalization of static feedback linearizability and a special case of a more general concept of flatness, can be checked by two…
We introduce a new definition of $\pi$-flatness for linear differential delay systems with time-varying coefficients. We characterize $\pi$- and $\pi$-0-flat outputs and provide an algorithm to efficiently compute such outputs. We present…
We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.
This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and twocontrols. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems…
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…
In this paper, we present a structurally flat triangular form which is based on the extended chained form. We provide necessary and sufficient conditions for an affine input system with two inputs to be static feedback equivalent to the…
This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a…
It is well known that for flat systems the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovsk\'y state are…
In this paper a class of simple, but nonlinear, systems of recursions involving $2$ dependent variables $x_{j}\left( n\right) $ is identified, such that the solutions of their initial-values problems -- with arbitrary initial data…