Passivity Equivalence of Siso Systems Via Continuous Feedback (original) (raw)

On the passivity of general nonlinear systems

In this article, we revisit the definitions of passivity and feedback passivity in the context of general continuous-time single input, single output, systems which are jointly nonlinear in the states and the control input. Neccessary conditions are given for the characterization of passive systems and extend the well known Kalman-Yakubovich-Popov (KYP) conditions. Passivity concepts are used for studying the stabilization problem of general nonlinear systems. We extend the 'Energy Shaping and Damping Injection' (ESDI) controller design methodology to the studied class of systems. A semicanonical form for nonlinear systems which is of the Generalized Hamiltonian type, including dissipation terms, is also proposed. Passive and strictly passive systems are shown to be easily characterized in terms of such a canonical form.

On the feedback passivity property of nonlinear discrete-time systems

The feedback passivity problem in nonlinear discrete-time systems is examined in this paper. The characteristics of the relative degree and zero dynamics of the nonpassive system are related to its feedback passivity property. The main contribution is the study of the relative degree properties of single-input single-output (SISO) passive systems in general form, and the use of them in the proposal of sufficient conditions to render this class of systems passive by means of a static state feedback control law. Some notes, based on previous results, referring the feedback passivity problem of multipleinput multiple-output (MIMO) nonlinear systems which are affine in the input are also given.

approach for nonlinear systems : Part II - System Theory

2009

This paper is second part of a survey on the basic notions and defini- tions of the infinite dimensional dierential geometric approach of (Fliess, Levine, Martin & Rouchon 1993, Pomet 1995). In this approach, a sys- tem is a infinite dimensional manifold. In the first part of this survey (Pereira da Silva, Silveira, Correa Filho & Batista 2008), one may find an elementary introduction about IR A -manifolds and dieties. In this second part, the notions of state representation and dynamic feedback are defined in an abstract manner, and then they reinterpreted in terms of coordinates and their corresponding equations. Instrumental in this setting are the dierent versions of the inverse function theorem, which are presented in this paper. The concept of subsystem is a key notion for establishing the definition of dynamic feedback and a new notion of regularity of implicit systems. This notion of regularity is shown to be useful for establishing a notion of equivalence between (implicit)...

Hybrid passivity and finite gain stability theorem: stability and control of systems possessing passivity violations

IET Control Theory & Applications, 2010

The stability and control of systems possessing passivity violations is considered. The authors seek to exploit the finite gain characteristics of a plant over a range in which a passive mapping no longer exists while implementing a similar hybrid passive and finite gain controller. Using the dissipative systems framework the authors define a hybrid system: one which possesses a passive map, and finite gain characteristics when the passive map is destroyed. The definition of a hybrid system utilises a switching parameter to break the system into passive and finite gain regions. It is shown that this switching parameter is equivalent to an ideal lowpass filter and can be approximated by a Butterworth filter. The stability of two hybrid systems within a negative feedback interconnection is also considered. A hybrid passivity and finite gain stability theorem is developed using both Lyapunov and input -output techniques, which yield equivalent results. Sufficient conditions for the closed-loop system to be stable are presented, which resemble an amalgamation of the traditional passivity and small-gain theorems.

Output-input stability and minimum-phase nonlinear systems

2000

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 particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of output-input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control.

Asymptotic stability of interconnected passive non‐linear systems

International Journal of Robust and Nonlinear Control, 1999

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

Passivity gains and the “secant condition” for stability

Systems & Control Letters, 2006

A generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems. The key is the introduction of a quantity that combines gain and phase information for each system in the cascade. For linear one-dimensional systems, the known result is recovered exactly.

Necessary Conditions for Feedback Passivation of Nonaffine-in-Control Systems

2013 Proceedings of the Conference on Control and its Applications, 2013

It is well understood that an open-loop Lyapunov stable nonaffine-in-control nonlinear system can be asymptotically stabilized through feedback. But stabilizing an open-loop unstable nonaffine system remains an open research question. This paper derives the necessary conditions required to render a general open-loop unstable nonlinear system passive through static feedback. It is shown that this is possible only if the system under consideration has relative degree one and is weakly minimum phase through an appropriate output definition. Unlike feedback passivation for affine-incontrol nonlinear systems this result is not sufficient. The developments and the essential ideas of the paper are verified for a continuously stirred tank reactor.

Systèmes non linéaires Nonlinear systems

2000

1.1 16 Pour tout renseignement s'adresser à : For further information, please contact: Topics 1. Embedded and networked systems Taking into account the network topology (multiple levels, different sizes and time scales) and constraints of communication. Development of new methodologies (modeling, control, state estimation of parameters) to ensure good performances, be robust to disturbances and reliable.