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Input-Output Invariants for Descriptor Systems

We study continuous-time and discrete-time descriptor systems from the time domain and frequency domain points of view. We present some input-output invariants for descriptor systems like transfer function, impulse and frequency responses, convolution and Hankel operators, Hankel singular values. These invariants are of great importance in robust control and approximation theory. Some norms for descriptor systems are introduced and their representations via the different input-output invariants are given.