Absolute Stability of Multivariable Lur'e-Type Descriptor Systems

The purpose of this paper is to derive conditions for absolute stability as well as existence of solutions for multivariable Lur’e-type feedback systems whose linear part is expressed by a descriptor system. The nonlinearities are uncertain and satisfy multivariable sector conditions, or a part of the nonlinearities satisfies a norm bounded condition. Thus, the systems can be refered to as multivariable Lur’e-type descriptor systems. In the existing works on Lur’e-type descriptor systems, the nonlinearities were assumed to be smooth or given as a set of single-variable scalar functions, while in this paper, the smoothness assumption is relaxed and multivariable vector-valued nonlinearities are considered. The obtained stability conditions are described in terms of linear matrix inequalities, which are extensions of the authors’ previous results on extended Popov criteria for multivariable Lur’e systems whose linear part is expressed by a state-space equation.