Abstract
This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector [a, b] in terms of linear matrix inequalities in its state-space realization matrices, which represent a generalization of similar conditions for bounded /spl Hscr//sub /spl infin//-norm systems. Further, a weaker definition of LTI systems strictly inside sector [a,b] is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems. >
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