Input-to-state stability of non-autonomous infinite-dimensional control systems

Abstract

<p style='text-indent:20px;'>This paper addresses input-to-state stability (ISS) and integral input-to-state stability (iISS) for non-autonomous infinite-dimensional control systems. With the notion of uniformly exponential stability scalar function, ISS and iISS are considered based on indefinite Lyapunov functions. In addition, we obtain several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities. As a result, the iISS criteria of non-autonomous bilinear systems is also established. Furthermore, an illustrative example is given to show the applicability of the results.</p>

Input‐to‐state practical stability for nonautonomous nonlinear infinite‐dimensional systems

“…The understanding of the nature of ISpS will be beneficial for the development of quantized and sample-data controllers for infinite-dimensional systems and will give further insights into the ISS theory of infinite-dimensional systems in References 14-21. Lyapunov-like characterizations for ISS of finite-dimensional systems described by ordinary differential equations (ODEs) were provided in References 11,12,22. The theory, especially the stability theory, for infinite-dimensional systems has been widely investigated due to the theory development of partial differential equations (PDEs), see References 14,15,18,20,23. In this article, we consider the ISpS for nonautonomous nonlinear infinite-dimensional systems and then obtain some novel criteria by using Lyapunov functions techniques and a nonlinear inequality. The contributions of this paper can be summed as follows.…”

“…Mironchenko 13 explored the characterizations of ISpS for a broad class of infinite‐dimensional systems using the uniform limit property and in terms of input‐to‐state stability. The understanding of the nature of ISpS will be beneficial for the development of quantized and sample‐data controllers for infinite‐dimensional systems and will give further insights into the ISS theory of infinite‐dimensional systems in References 14‐21. Lyapunov‐like characterizations for ISS of finite‐dimensional systems described by ordinary differential equations (ODEs) were provided in References 11,12,22.…”

“…Lyapunov‐like characterizations for ISS of finite‐dimensional systems described by ordinary differential equations (ODEs) were provided in References 11,12,22. The theory, especially the stability theory, for infinite‐dimensional systems has been widely investigated due to the theory development of partial differential equations (PDEs), see References 14,15,18,20,23.…”