Dissipative differential inclusions, set-valued energy storage and supply rate maps, and discontinuous dynamical systems

2012 ◽  
Author(s):  
W. M. Haddad ◽  
T. Sadikhov
Keyword(s):  
Energy Storage ◽  
Dynamical Systems ◽  
Differential Inclusions ◽  
Supply Rate ◽  
Dissipative Differential Inclusions

Large-Scale Impulsive Dynamical Systems

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Functions ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Supply Rate ◽  
Nonlinear Dynamical ◽  
Dissipation Inequality ◽  
Vector Lyapunov Functions ◽  
Definition Of ◽  
Stability Results

This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear impulsive dynamical systems in terms of a hybrid vector dissipation inequality involving a vector hybrid supply rate, a vector storage function, and an essentially nonnegative, semistable dissipation matrix. The chapter also defines generalized notions of a vector available storage and a vector required supply and shows that they are element-by-element ordered, nonnegative, and finite. Extended Kalman-Yakubovich-Popov conditions, in terms of the local impulsive subsystem dynamics and the interconnection constraints, are developed for characterizing vector dissipativeness via vector storage functions for large-scale impulsive dynamical systems. Finally, using the concepts of vector dissipativity and vector storage functions as candidate vector Lyapunov functions, the chapter presents feedback interconnection stability results of large-scale impulsive nonlinear dynamical systems.

On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions

2007 ◽  
Vol 16 (5-6) ◽  
pp. 651-671 ◽  
Author(s):  
Desheng Li ◽  
Yejuan Wang ◽  
Suyun Wang
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusions

Filippov–Pliss lemma and m-dissipative differential inclusions

2012 ◽  
Vol 56 (4) ◽  
pp. 1707-1717 ◽  
Author(s):  
Qamar Din ◽  
Tzanko Donchev ◽  
Dimitar Kolev
Keyword(s):  
Differential Inclusions ◽  
Dissipative Differential Inclusions

scholarly journals Robust dissipativity for uncertain impulsive dynamical systems

2003 ◽  
Vol 2003 (3) ◽  
pp. 119-128 ◽  
Author(s):  
Bin Liu ◽  
Xinzhi Liu ◽  
Xiaoxin Liao
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Supply Rate

We discuss the robust dissipativity with respect to the quadratic supply rate for uncertain impulsive dynamical systems. By employing the Hamilton-Jacobi inequality approach, some sufficient conditions of robust dissipativity for this kind of system are established. Finally, we specialize the obtained results to the case of uncertain linear impulsive dynamical systems.

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