Pdf dissipativity theory and stability of feedback. The key foundation in developing dissipativity theory for general nonlinear dynamical systems was. The classical interconnections theorems of linearquadratic dissipativity. Vector dissipativity theory and stability of feedback interconnections. Dissipativity and stability of interconnections dissipativity and stability of interconnections fradkov, alexander l leonov, gennady 20070325 00. This principle allows to prove stability of a closed system by viewing it as the interconnection of two. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of leftcontinuous dynamical systems. The results demonstrate that if a nonlinear system c or d is qsr dissipative 14, then its linearization is qsr dissipative as well. However, numerous engineering applications give rise to discontinuous dynamical systems. This paper deals with the dissipativity of the solutions on nonlinear neutral functionaldifferetial equations. In section 4, feedback interconnection of hybrid input output automata over a network with delays is considered.
Dissipativity theory along with lyapunov stability theory for feedback interconnections of dissipative systems has been extensively developed for dynamical systems possessing continuous flows. Section 3 presents results on the stability of interconnections of dissipative hybrid systems. In this paper we build on these results to develop general stability criteria for feedback interconnections of nonlinear. In this paper, we develop an analysis framework for discretetime largescale dynamical systems based on vector dissipativity notions. Relevant examples are provided when needed to motivate the theory or demonstrate how it can be applied in practice. Stability and dissipativity theory for nonnegative dynamical systems. Dissipativity theory and stability of feedback interconnectionsfor hybrid dynamical systems by wassim m. Chapter 2 derives a stability test for interconnected systems from the dissipativity. Basic input, state, and output properties, and finitetime stability of feedback interconnections. Dissipativity based analysis using dynamic supply rates. Stability of interconnected switched systems using qsr.
Dissipativity theory plays a fundamental role in the stability analysis of feedback interconnections of dynamical systems 17. Stability of locally dissipative interconnected systems ieee xplore. And when you want to do more, subscribe to acrobat pro. It is proven that dissipativity is equivalent to the existence of a non. Largescale dissipative and passive control systems in. Lecture notes in control and information sciences, vol. These results generalize the positivity and small gain theorems to the case of leftcontinuous, hybrid, and impulsive dynamical systems. Dissipativity and stability analysis using rational. The result has an immediate application in studying the powersystem transient stability problem and can. Dissipativity and stability of interconnections wiley online library. Request pdf dissipative and stability of interconnections a new definition of dissipativity is proposed. Dissipativity theory and stability of feedback interconnections for hybrid dynamical systems. Stability, dissipativity, and optimal control of discontinuous dynamical systems approved by.
For example, two of the most fundamental results concerning stability of feedback systems are the positivity and small gain theorems 812 which are a special case of dissipativity theory. Dynamic dissipativity theory for stability of nonlinear. The concept of symmetry is employed as a powerful tool to overcome the complexity of multiagent systems by reducing the number of multiple interconnections. Dissipativity theory for hybrid systems with applications to networked control systems doctoral dissertation. We will therefore pay particular attention to the case in which the storage is nonnegative. Put di erently, we exploit dissipativity concepts to establish a relation 1 indeed the origins of optimal control theory can be traced back at least for another 300 years to the 17th century. Abstract of dissertation stability analysis of recurrent neural networks with applications recurrent neural networks are an important tool in the analysis of data with temporal structure. Dissipativity and exponentially asymptotic stability of. Solution properties of the largescale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. Vector dissipativity theory and stability of feedback. Furthermore, we develop new notions of dissipativity theory for nonnegative dynamical systems with time delay using linear storage functionals with linear supply rates. Vector dissipativity theory for discretetime largescale. Dissipative and stability of interconnections request pdf.
The use of inputoutput properties and interconnection matrices for network stability tests dates back to the early refs. Specifically, using vector storage functions and vector supply rates, dissipativity properties of the discretetime composite largescale system are shown to be determined from the dissipativity properties of the subsystems and their interconnections. Partial stability of statedependent impulsive dynamical systems. This assumption can be relaxed into more general dissipativity to show the stability of. Dissipativitypassivity based control design for symmetric. General stability criteria are given for lyapunov and asymptotic stability of feedback largescale impulsive dynamical systems. These systems are usually interpreted as hybrid systems. Using the concepts of dissipativity and exponential dissipativity for impulsive systems, in this chapter we develop feedback interconnection stability results for nonlinear impulsive dynamical systems. Request pdf nonlinear impulsive dynamical systems part i.
Qsrdissipativity, a general test may be applied to determine whether a feedback interconnection is stable 7, 8. Vector dissipativity theory and stability of feedback interconnections for largescale nonlinear dynamical systems wassim m. Our goal is to derive a bottomup stability test using dissipativity properties and. Vector dissipativity theory and stability of feedback interconnections for largescale nonlinear dynamical systems july 2004 international journal of control 7710. Dissipativity theory for hybrid systems with applications. In a companion paper nonlinear impulsive dynamical systems. Haddad, chairman aerospace engineering georgia institute of technology dr. For global stability, these supply rates must be compatible, i.
Dissipativity theory for discontinuous dynamical systems. Complex systems, which consist of different interdependent and interlocking subsystems, typically have multiple equilibrium points associated with different set points of each operation mode. Q 1 a r2 stability testing of new drug substances and. Stability of timedependent impulsive dynamical systems. Dissipativity a generalization of passivity of a nonlinear system and its linearization is studied in 7.
Group and total dissipativity and stability of multiequilibria hybrid automata navarrolopez, e. Aps, m the mosek optimization toolbox for matlab manual. Both the cases of constant as well as time varying delays are addressed. Pdf this note extends the results of the existing dissipative systems theory to include locally dissipative systems.
Group and total dissipativity and stability of multi. In chapters 2 and 3 stability and dissipativity theory for nonlinear impulsive dynamical systems was developed. For example, hill and moylan 1977 assumes the q, s, r dissipativity in each subsystem, which is defined by the supply rate s. It is purely in terms of the rate of supply that goes in and out of a dynamical system. Haddad and vijaysekhar chellaboina no static citation data no static citation data cite. Abstract a new definition of dissipativity is proposed. Differential dissipativity theory for dominance analysis. Specifically, using linear lyapunov functions we develop necessary and sufficient conditions for lyapunov stability, semistability. Dissipativity and stability of interconnections willems. Stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for nonlinear impulsive dynamical. By using the qsr decomposable dissipativity approach, we present stability results for the feedback interconnection of two dissipative switched systems.
Furthermore, we generalize dissipativity theory to nonlinear dynamical systems with impulsive effects. Hence, by establishing l 2gain or passivity properties of piecewise linear systems we can hope to establish stability of interconnections by invoking small gain and passivity theorems. Passivity and dissipativity of a nonlinear system and its. Pdf dissipativity theory for discontinuous dynamical. Pendharkar bombardier transportation switzerland, brownboveri strasse 5, 8050 zurich, switzerland. Communications in applied analysis 18 2014 455522 nonlinear differential equations with discontinuous righthand sides. Resonance stability in electrical rai lway systems a dissipativity approach i. Stability and dissipativity theory for nonnegative. In this paper we develop lyapunov and invariant set stability theorems for nonlinear impulsive dynamical systems. We study symmetries in the design of largescale dissipative and passive control. Chapter 2 derives a stability test for interconnected systems from the dissipativity characteristics of the subsystems.
The ability of recurrent networks to model temporal data and act as dynamic mappings makes them ideal for application to complex control problems. This result is a generalization of both the passivity theorem and the small gain theorem and may be applied to a large class of interconnections including interconnections that dont. These results are then used to develop general stability criteria for feedback interconnections of. This approach is particularly powerful when one exploits the structure of the interconnection and identi. Networks of dissipative systems eecs at uc berkeley. Dissipativity reinforcement in interconnected systems. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of leftcontinuous systems. Pdf stability of locally dissipative interconnected systems. Pdf group and total dissipativity and stability of multi. Stability and dissipativity lyapunov and invariant set stability theorems and dissipativity theory were developed for nonlinear impulsive dynamical systems. Dissipativity and stability of interconnections willems 2007. Finally, these results are used to develop feedback interconnection stability results for largescale nonlinear dynamical systems using vector lyapunov functions. Design of cyberphysical systems using passivitydissipativity.
In the framework of dissipativity and passivity theory, stability conditions for largescale systems are derived by categorizing agents into symmetry groups and applying local control laws under limited interconnections. Stability of the feedback interconnection of two dissipative systems can be assessed stability using dissipativity if g 1 is dissipative with q 1,s 1,r 1 and g 2 is dissipative with q 2,s 2,r 2, the feedback interconnection of the two systems is stable if the following lmi is satisfied this can also be seen as a control design tool. Vector dissipativity theory for largescale impulsive. Published pdf deposited in coventry university repository january 2017. Abstract we propose a theory for stability analysis of railway systems based on energy exchange principles between. Eric feron aerospace engineering georgia institute of technology dr. Objectives of the guideline the following guideline is a revised version of the ich q1a guideline and defines the stability data package for a new drug substance or drug product that is sufficient for a. Dissipativity and stability of interconnections citeseerx. Only with adobe acrobat reader you can view, sign, collect and track feedback, and share pdfs for free. Stability of dissipative interconnections home pages of esat ku.
Impulsive and hybrid dynamical systems goes beyond similar treatments by developing invariant set stability theorems, partial stability, lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energybased hybrid control, optimal control, disturbance rejection control, and robust control for. Some contractive inequalities of the solutions are obtained, which guarantee the exponentially asymptotic stability of the solutions. Both allow stability of a feedback interconnection to be verified from the analysis of its components. These properties provide powerful stability results for single systems and interconnections of systems. Dissipativity based stability conditions of a network of subsystems are established based on the supply rates of the subsystems and their interconnections. In this paper we develop several results on stability, dissipativity, and stability of feedback interconnections of linear and nonlinear nonnegative dynamical systems. Differential dissipativity theory for dominance analysis fulvio forni, rodolphe sepulchre.
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