Proportional and proportional-derivative canonical forms for descriptor systems with outputs

We construct a new canonical form for descriptor systems (E, A, B, C) under proportional state feedback, proportional output injection and changes of bases in the input space, the output space, the state space (domain) and the state equation space (codomain). Geometric characterizations of the invariants are given. Four pencils are introduced in order to point out the relationships with Kronecker's theory of matrix pencils. This finally allows us to define canonical forms under proportional plus derivative action.

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