ISDS small-gain theorem and construction of ISDS Lyapunov functions for interconnected systems
نویسندگان
چکیده
We consider networks of input-to-state dynamically stable (ISDS) systems and use a small-gain condition to assure the ISDS property for their interconnection. Under this small-gain condition we provide a construction of an ISDS Lyapunov function including explicit derivation of corresponding rates and gains for the whole interconnection. © 2010 Elsevier B.V. All rights reserved.
منابع مشابه
Quasi-ISS/ISDS observers for interconnected systems and applications
This paper considers interconnected nonlinear dynamical systems and studies observers for such systems. For single systems the notion of quasi-input-to-state dynamical stability (quasi-ISDS) for reduced-order observers is introduced and observers are investigated using error Lyapunov functions. It combines the main advantage of ISDS over input-to-state stability (ISS), namely the memory fading ...
متن کاملMPC Schemes Guaranteeing ISDS and ISS for Nonlinear (Time-Delay) Systems
New directions in model predictive control MPC are introduced. On the one hand, we combine the input-to-state dynamical stability ISDS with MPC for single and interconnected systems. On the other hand, we introduceMPC schemes guaranteeing input-to-state stability ISS of single systems and networks with time delays. In both directions, recent results of the stability analysis from thementioned a...
متن کاملAn invariance kernel representation of ISDS Lyapunov functions
We apply set valued analysis techniques in order to characterize the input–to–state dynamical stability (ISDS) property, a variant of the well known input–to–state stability (ISS) property. Using a suitable augmented differential inclusion we are able to characterize the epigraphs of minimal ISDS Lyapunov functions as invariance kernels. This characterization gives new insight into local ISDS p...
متن کاملA Constructive Proof of ISS Small-Gain Theorem using Generalized Scaling
This paper presents a Lyapunov-type proof of the Input-toState Stable(ISS) small-gain theorem. The proof given in this paper demonstrates how to construct a Lyapunov function explicitly, which contrasts with existing proofs based on input-output analysis. The Lyapunov functions are constructed by selecting state-dependent scaling functions properly. The construction of Lyapunov functions motiva...
متن کاملA Lyapunov-based small-gain theorem for interconnected switched systems
Stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems theremay exist some subsystems that are not input-to-state stable (nonISS). We show that, providing the switching signals neither switch too frequently nor activate non-ISS subsystems for too long, a small-gain theorem can be used to conclude global asymptotic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Systems & Control Letters
دوره 59 شماره
صفحات -
تاریخ انتشار 2010