About robust hyperstability and dissipativity of linear time-invariant dynamic systems subject to hyperstable controllers and unstructured delayed state and output disturbances

Abstract

This paper considers the robust asymptotic closed-loop hyperstability of a nominal time-invariant plant with an associate strongly positive real transfer function subject to unstructured disturbances in the sate and output. Such disturbances are characterized by upper-bounding growing laws of the state and control. It is assumed that the controller is any member within a class which satisfies a Popov´s type integral inequality. The continuous-time nonlinear and perhaps time-varying feedback controllers belong to a certain class which satisfies a discrete-type Popov´s inequality. The robust closed-loop hyperstability property is proved under certain explicit conditions of smallness of the coefficients of the upper-bounding functions of the norms of the unstructured disturbances related to the absolute stability abscissa of the modelled part of the nominal feed-forward transfer function.

Keywords

• hyperstability
• asymptotic hyperstability
• popov′s inequalities
• positive real transfer function
• strictly positive real transfer function
• robustness