The persistence of excitation of signals generated by time-invariant, autonomous, linear, and nonlinear systems is studied using a geometric approach. A rank condition is shown to be equivalent, under certain assumptions, to the persistence of excitation of the solutions of the class of systems considered, both in the discrete-time and in the continuous-time settings. The rank condition is geometric in nature and can be checked a priori, i.e. without knowing explicitly the solutions of the system, for almost periodic systems. The significance of the ideas and tools presented is illustrated by means of simple examples. Applications to model reduction from input-output data and stability analysis of skew-symmetric systems are also discussed.

The persistence of excitation of signals generated by time-invariant, continuous-time, autonomous linear and nonlinear systems is studied. The notion of persistence of excitation is characterised as a rank condition which is reminiscent of a geometric condition used to study the controllability properties of a control system. The notions and tools introduced are illustrated by means of simple examples and of an application in system identification.

Abstract-The problem of identifying deterministic autonomous linear and nonlinear systems is studied. A specific version of the theory of deterministic subspace identification for discrete-time autonomous linear systems is developed in continuous time. By combining the subspace approach to linear identification and the differentialgeometric approach to nonlinear control systems, a novel identification framework for continuous-time autonomous nonlinear systems is developed.

The differential L2,p gain of a linear, timeinvariant, p-dominant system is shown to coincide with the H∞,p norm of its transfer function G, defined as the essential supremum of the absolute value of G over a vertical strip in the complex plane such that p poles of G lie to right of the strip. The close analogy between the H∞,p norm and the classical H∞ norm suggests that robust dominance of linear systems can be studied along the same lines as robust stability. This property can be exploited in the analysis and design of nonlinear uncertain systems that can be decomposed as the feedback interconnection of a linear, time-invariant system with bounded gain uncertainties or nonlinearities.

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