It is shown that a discrete-time system may be linearizable by exogenous dynamic feedback, even if it cannot be linearized by endogenous feedback. This property is completely unexpected and constitutes a fundamental difference with respect to the continuous-time case. The notion of exogenous linearizing output is introduced. It is shown that existence of an exogenous linearizing output is a suf...

Many practical applications including speech and audio processing, signal processing, system identification, econometrics and time series analysis involve the problem of reconstructing a dynamic system model from data observed with noise in all variables. We consider an important class of dynamic single-input single-output nonlinear systems where the system model is polynomial in observations b...

We extend the notion of dissipative dynamical systems to formalize the concept of the nonlinear analog of strict positive realness and strict bounded realness. In particular, using exponentially weighted system storage functions with appropriate exponentially weighted supply rates, we introduce the concept of exponential dissipativity. The proposed results provide a generalization of the strict...

Integrability and linearizability of polynomial differential systems are studied. The computation of generalized period constants is a way to find necessary conditions for linearizable systems for any rational resonance ratio. A method to compute generalized period constants is given. The algorithm is recursive and easy to realize with computer algebraic system. As the application, we discuss l...

A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step recurrence relation, integral inter-relations, and quasi-orthogonality relations. 1. Motivation The understanding of matrix-valued orthogonal polynomi...

We consider a nonlinear semi–classical Schrödinger equation for which quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. The relevance of the nonlinearity was discussed by R. Carles, C. Fermanian–Kammerer and I. Gallagher for L-supercritical power-like nonlinearities and more general initial data. The present results concern the L-critical case, ...

Analysis of exclusively-kinetic two-link underactuated mechanical systems is undertaken in this paper. It is first shown that such systems are not full-state feedback linearizable around any equilibirium point. Also, the equilibrium points for which the system is small-time locally controllable (STLC) is at most a one dimensional submanifold. A concept less restrictive than STLC, termed the sma...

The problem of quadratic stabilization of a class of nonlinear systems will be examined in this paper. By employing a well-known Riccati approach, we develop a technique for designing a state feedback control law which quadratically stabilizes the system for all admissible uncertainties. This state feedback control law consists of linear and nonlinear feedback control terms. The linear feedback...

In this paper, we present a design procedure of composite nonlinear feedback control for general multivariable systems with actuator saturation. We consider both the state feedback case and the measurement feedback case without imposing any restrictive assumption on the given systems. The composite nonlinear feedback control consists of a linear feedback law and a nonlinear feedback law without...