Output feedback strict passivity of discrete-time nonlinear systems and adaptive control system design with a PFC

In this paper, a passivity-based adaptive output feedback control for discrete-time nonlinear systems is considered. Output Feedback Strictly Passive (OFSP) conditions in order to design a stable adaptive output control system will be established. Further, a design scheme of a parallel feedforward compensator (PFC), which is introduced in order to realize an OFSP controlled system, will be provided and an adaptive output feedback control system design scheme with a PFC will be proposed.     

基于输出严格无源的切换非线性系统的H∞ 分析

针对切换非线性系统,考虑了基于输出严格无源性的 ∞问题.利用每个子系统的输出严格无源性(这里并不要求每个子系统都在整个时间域上满足输出严格无源性,只要求子系统在其激活时间段内满足输出严格无源性),同时借助切换系统理论中的多 Lyapunov 函数方法,用输出严格无源性中的存储函数作为备选的多 Lyapunov 函数,设计了依赖存储函数的最小切换规则,研究了一类切换非线性系统的 ∞问题,给出了存在 ∞性能指标的充分条件.此外,这种基于输出严格无源性的方法也可用于分析切换级联系统的 ∞问题.最后,通过仿真算例验证了这种基于输出严格无源性的方法的有效性.     

An analytical approach to one-parameter MIMO systems passivity enforcement

Stable linear time-invariant systems can be made passive by a feedforward action. In this article, an analytical approach to obtain the matrix which allows to enforce passivity in the system is proposed. This matrix depends only on one parameter, namely α. The introduced method is based on the calculation of the characteristic polynomial of the Hamiltonian matrix associated to the Positive Real problem. This polynomial is then used to derive a finite set of values of the parameter α, in which the value assuring passivity enforcement with minimum dissipation can be selected. Numerical examples are reported.     

The strict bounded real lemma in infinite dimensions

The strict bounded real lemma is generalized to an infinite-dimensional setting. This relates the existence of a stabilizing solution to a Riccati equation to an H∞-norm bound and to the existence of a solution to a Riccati inequality.     

A new result on passivity preserving model reduction

The problem of model reduction with preservation of passivity is investigated. The approach is based on positive real interpolation, and is inspired by the similarity between Löwner and Pick matrices. The former are important in problems of general rational interpolation while the latter in problems of interpolation by positive real functions. It follows that interpolation of the original set of data together with an appropriately defined mirror-image set of data yields automatically positive real interpolants. Subsequently, we show how this result can be implemented using a Krylov projection procedure. The ensuing model reduction method preserves stability and passivity and can be implemented efficiently for the large-scale systems.     

A stability and contractiveness analysis of discrete-time Markovian jump linear systems

We propose performance criteria for discrete-time linear systems with Markov jumping parameters. Exact convex conditions for internal stability and contractiveness of such systems are expressed in terms of linear matrix inequalities. These conditions are of the same form as that in the Kalman-Yacubovich-Popov lemma.     

A global state feedback output regulating control for uncertain systems in strict feedback form

A family of single-input, single-output, nonlinear systems in strict feedback form with uncertain constant parameters which appear linearly and belong to a known compact set Π is considered. A global robust output regulation problem via state feedback is addressed and solved under the assumptions that the regulator equations are solvable in Π, the output equation does not depend on uncertain parameters, no modelled disturbances affect the system and the output reference signal is generated by a known exosystem whose state is bounded and available for feedback. Robust adaptive techniques are used to guarantee closed loop boundedness and to achieve, without requiring persistency of excitation, global asymptotic output regulation for a class of feedback linearizable systems which may have unbounded uncertain tracking dynamics or may not have a well-defined global relative degree.     

On relationships among passivity,positive realness,and dissipativity in linear systems

The notions of passivity and positive realness are fundamental concepts in classical control theory, but the use of the terms has varied. For LTI systems, these two concepts capture the same essential property of dynamical systems, that is, a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment. This paper summarizes the connection between these two concepts for continuous and discrete time LTI systems. Beyond that, relationships are provided between classes of strictly passive systems and classes of positive real systems. The more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy-based results. The frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity. After surveying relevant existing results, some clarifying results are presented. These involve connections between classes of passive systems and finite-gain _L2$L_2$ stability as well as asymptotic stability. Additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results. This paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts.     

The positive real lemma and construction of all realizations of generalized positive rational functions

We here extend the well known positive real lemma (also known as the Kalman-Yakubovich-Popov lemma) to a complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. All state space realizations are partitioned into subsets, each is identified with a set of matrices satisfying the same Lyapunov inclusion. Thus, each subset forms a convex invertible cone, and is in fact is replica of all realizations of positive functions of the same dimensions. We then exploit this result to provide an easy construction procedure of all (not necessarily minimal) state space realizations of generalized positive functions. As a by-product, this approach enables us to characterize systems which can be brought, through a static output feedback, to be generalized positive.