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**1 - 5**of**5**### Dissipativity Analysis of Linear State/Input Delay Systems

"... This paper discusses dissipativity problem for system of linear state/input delay equations. Motivated by dissipativity theory of control systems, we choose a new quadratic supply rate. Using the concept of dissipativity, necessary and sufficient conditions for the linear state/input delay systems ..."

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This paper discusses dissipativity problem for system of linear state/input delay equations. Motivated by dissipativity theory of control systems, we choose a new quadratic supply rate. Using the concept of dissipativity, necessary and sufficient conditions for the linear state/input delay systems to be dissipative and exponentially dissipative are derived. The connection of dissipativity with stability is also considered. Finally, passivity and finite gain are explored, correspondingly. The positive-real and bounded-real lemmas are derived.

### CONDITIONS FOR THE EXISTENCE OF CONTINUOUS STORAGE FUNCTIONS FOR NONLINEAR DISSIPATIVE SYSTEMS

"... Abstract The problem of existence of continuous storage functions for dissipative nonlinear systems is considered. It is shown that, if a nonlinear system is dissipative in the state x * , then, under certain assumptions, a continuous storage function can be constructed on a set of points accessibl ..."

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Abstract The problem of existence of continuous storage functions for dissipative nonlinear systems is considered. It is shown that, if a nonlinear system is dissipative in the state x * , then, under certain assumptions, a continuous storage function can be constructed on a set of points accessible from x * by concatenation of a finite number of forward and backward motions of the system. Most of these assumptions are weaker than certain controllability-type properties and can be checked using similar tests.

### Finite L2-gain with Nondifferentiable Storage Functions

"... We consider affine control systems with the finite L2-gain property in the case the storage function is nondifferentiable. We generalize some classical results concerning the connection of the finite L2-gain property with the stability properties of the unforced system, the characterization of finit ..."

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We consider affine control systems with the finite L2-gain property in the case the storage function is nondifferentiable. We generalize some classical results concerning the connection of the finite L2-gain property with the stability properties of the unforced system, the characterization of finite L2gain by means of partial differential inequalities of the Hamilton-Jacobi type and the problem of giving to a system the finite L2-gain property by means of a feedback law. Moreover, we introduce and study the apparently new notion of exact storage function. Keywords: L2-gain; nondifferentiable storage functions; Filippov solutions 1

### unknown title

, 2004

"... www.elsevier.com/locate/sysconle Conditions for the existence of continuous storage functions for nonlinear dissipative systems ..."

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www.elsevier.com/locate/sysconle Conditions for the existence of continuous storage functions for nonlinear dissipative systems

### FURTHER RESULTS ON THE EXISTENCE OF A CONTINUOUS STORAGE FUNCTION FOR NONLINEAR DISSIPATIVE SYSTEMS

"... linear systems, Local w-uniform reachability, Weak acces-sibility The problem of existence of continuous storage function for dissipative nonlinear systems is considered. It is shown that, if a nonlinear system is dissipative in the state x∗, then, under certain assumptions, a continuous storage fun ..."

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linear systems, Local w-uniform reachability, Weak acces-sibility The problem of existence of continuous storage function for dissipative nonlinear systems is considered. It is shown that, if a nonlinear system is dissipative in the state x∗, then, under certain assumptions, a continuous storage function can be constructed on a set of points accessi-ble from x ∗ by concatenation of a finite number of for-ward and backward motions of the system. Most of these assumptions are weaker than certain controllability-type properties and can be checked by the similar tests. 1