1,721,214 research outputs found
Minimal representations of continuous-time processes having spectral density with zeros in the extended imaginary axis
No full textGiven a process y with stationary increments and rational incremental spectral density P, we parametrizes minimal state-space representations of dy.
We consider the case when P may have zeros on the imaginary axis including infinity and we analyze the zero structure of each state-space representation
A parametrization of the minimal square spectral factors of a nonrational spectral density.
No full text
Positive real lemma: necessary and sufficient conditions for the existence of solutions under virtually no assumptions
No full textIn this note, the celebrated positive real lemma equations are considered with the purpose of obtaining necessary and sufficient conditions for the existence of solutions under the mildest system-theoretic assumptions. More precisely, necessary and sufficient conditions are established under the very weak assumption of sign-controllability. It is then shown that the order of the equations may be suitably reduced by restricting attention to a subspace related to a certain observable subsystem. This reduction, beside being interesting per se, permits us to weaken the assumption of sign-controllability. Finally, the assumptions are further weakened as to include the case when the state matrix has uncontrollable eigenvalues on the imaginary axis
On the structure of the solutions of discrete-time algebraic Riccati Equation with singular closed-loop matrix
No full textThe classical discrete-time algebraic Riccati equation (DARE) is considered in the case when the corresponding closed-loop matrix is singular. It is shown that in this case all the symmetric solutions of the DARE coincide along some directions.
A parametrization of the set of solutions in terms of the reduced-order DARE is then obtained.
This parametrization provides an algorithm (that appears to be computationally very attractive when the multiplicity of the zero eigenvalue of the closed-loop matrix is large) for the computation of the solutions of the DARE.
The same issue for the generalized DARE is also addressed
Optimal steering for an extended class of nonholonomic systems using Lagrange functionals
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