Strong input-to-state stability for infinite-dimensional linear systems

Nabiullin, Robert; Schwenninger, Felix L.

doi:10.1007/s00498-018-0210-8

Cited by 15 publications

(22 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following result shows that in the case of linear systems (integral) ISS can be characterized by exponential stability and admissibility in certain norms. For a generalization of this theorem for non-exponentially stable semigroups, see [31]. Using Theorem 19, Proposition 4 has the following version.…”

Section: Applications To Input-to-state Stabilitymentioning

confidence: 99%

“…Remark 23. Corollary 21 can be generalized to the weaker notions of 'strong inputto-state stability' and 'strong integral ISS' which are discussed in [31]. In these notions, exponential stability of the semigroup is replaced by strong stability and the result follows as above by using a generalization of Theorem 19 from [31].…”

Section: Applications To Input-to-state Stabilitymentioning

confidence: 99%

See 1 more Smart Citation

On continuity of solutions for parabolic control systems and input-to-state stability

Jacob

Schwenninger

Zwart

2019

Journal of Differential Equations

Self Cite

View full text Add to dashboard Cite

We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial differential equations. Here, we focus on parabolic equations which allow for operator-theoretic methods such as the holomorphic functional calculus. Moreover, we investigate stronger conditions than continuity leading to input-to-state stability with respect to Orlicz spaces. This also implies that the notions of input-to-state stability and integral-input-to-state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite-dimensional.

show abstract

Section: Applications To Input-to-state Stabilitymentioning

confidence: 99%

Section: Applications To Input-to-state Stabilitymentioning

confidence: 99%

On continuity of solutions for parabolic control systems and input-to-state stability

Jacob

Schwenninger

Zwart

2019

Journal of Differential Equations

Self Cite

View full text Add to dashboard Cite

show abstract

“…In recent years, these last two notions of strong and especially of uniform input-to-state stability have been intensively studied. See, for instance, [2], [10], [11], [12], [14], [5], [6], [15], [9], [13], [20], [7], [8], [23], [24] and the references therein. Also, weak input-to-state stability can be established for a rather large class of semilinear systems (both in the case of inputs entering in the domain and in the case of inputs entering at the boundary of the domain on which the partial differential equation describing the system lives).…”

Section: Introductionmentioning

confidence: 99%

Weak input-to-state stability: characterizations and counterexamples

Schmid

2019

Math. Control Signals Syst.

View full text Add to dashboard Cite

We establish characterizations of weak input-to-state stability for abstract dynamical systems with inputs, which are similar to characterizations of uniform and of strong input-to-state stability established in a recent paper by A. Mironchenko and F. Wirth. We also answer, by means of suitable counterexamples, two open questions concerning weak input-to-state stability (and its relation to other common stability concepts) raised in the aforementioned paper.

show abstract

“…More recently, the investigation of the ISS of infinite-dimensional systems is seeing a rapid growth. Important and interesting results obtained include characterizations of ISS and iISS for a rather general class of infinite-dimensional nonlinear systems, applications of ISS-Lyapunov theory for studying various classes of PDE systems [17,18,22,19,20,21]. In detail, in doctoral dissertation [22], Nabiullin considered the ISS and iISS, and their relationships, of infinite-dimensional linear systems.…”

mentioning

confidence: 99%

“…Important and interesting results obtained include characterizations of ISS and iISS for a rather general class of infinite-dimensional nonlinear systems, applications of ISS-Lyapunov theory for studying various classes of PDE systems [17,18,22,19,20,21]. In detail, in doctoral dissertation [22], Nabiullin considered the ISS and iISS, and their relationships, of infinite-dimensional linear systems. In [19], the authors explored the characterizations of iISS for infinite-dimensional bilinear systems and further studied the characterizations of ISS for semilinear infinite-dimensional systems in [20,21].…”

mentioning

confidence: 99%

Input-to-state stability of infinite-dimensional stochastic nonlinear systems

Wang¹,

Zhang²,

Su³

2022

DCDS-B

View full text Add to dashboard Cite

In this paper, the input-to-state stability (ISS), stochastic-ISS (SISS) and integral-ISS (iISS) for mild solutions of infinite-dimensional stochastic nonlinear systems (IDSNS) are investigated, respectively. By constructing a class of Yosida strong solution approximating systems for IDSNS and using the infinite-dimensional version Itô's formula, Lyapunov-based sufficient criteria are derived for ensuring ISS-type properties of IDSNS, which extend the existing corresponding results of infinite-dimensional deterministic systems. Moreover, two examples are presented to demonstrate the main results.

show abstract

Strong input-to-state stability for infinite-dimensional linear systems

Cited by 15 publications

References 15 publications

On continuity of solutions for parabolic control systems and input-to-state stability

On continuity of solutions for parabolic control systems and input-to-state stability

Weak input-to-state stability: characterizations and counterexamples

Input-to-state stability of infinite-dimensional stochastic nonlinear systems

Contact Info

Product

Resources

About