Behavioral realizations using companion matrices and the smith form

This is the author accepted manuscript. The final version is available from Society for Industrial and Applied Mathematics via the DOI in this record.Classical procedures for the realization of transfer functions are unable to represent uncontrollable behaviors. In this paper, we use companion matrices and the Smith form to derive explicit observable realizations for a general (not necessarily controllable) linear time-invariant be- havior. We then exploit the properties of companion matrices to efficiently compute trajectories, and the solutions to Lyapunov equations, for the realizations obtained. The results are motivated by the important role played by uncontrollable behaviors in the context of physical systems such as passive electrical and mechanical networks

Behavioral realizations using companion matrices and the smith form

Classical procedures for the realization of transfer functions are unable to represent uncontrollable behaviors. In this paper, we use companion matrices and the Smith form to derive explicit observable realizations for a general (not necessarily controllable) linear time-invariant behavior. We then exploit the properties of companion matrices to efficiently compute trajectories, and the solutions to Lyapunov equations, for the realizations obtained. The results are motivated by the important role played by uncontrollable behaviors in the context of physical systems such as passive electrical and mechanical networks.This is the author accepted manuscript. The final version is available from SIAM via https://doi.org/ 10.1137/14099191

On the internal signature and minimal electric network realizations of reciprocal behaviors

In a recent paper, it was shown that (i) any reciprocal system with a proper transfer function possesses a signature-symmetric realization in which each state has either even or odd parity; and (ii) any reciprocal and passive behavior can be realized as the driving-point behavior of an electric network comprising resistors, inductors, capacitors and transformers. These results extended classical results to include uncontrollable systems. In this paper, we establish new lower bounds on the number of states with even parity (capacitors) and odd parity (inductors) for reciprocal systems that need not be controllable

On the internal signature and minimal electric network realizations of reciprocal behaviors

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In a recent paper, it was shown that (i) any reciprocal system with a proper transfer function possesses a signature-symmetric realization in which each state has either even or odd parity; and (ii) any reciprocal and passive behavior can be realized as the driving-point behavior of an electric network comprising resistors, inductors, capacitors and transformers. These results extended classical results to include uncontrollable systems. In this paper, we establish new lower bounds on the number of states with even parity (capacitors) and odd parity (inductors) for reciprocal systems that need not be controllable

On the optimal control of passive or non-expansive systems

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.The positive-real and bounded-real lemmas solve two important linear-quadratic optimal control problems for passive and non-expansive systems, respectively. The lemmas assume controllability, yet a passive or non-expansive system can be uncontrollable. In this paper, we solve these optimal control problems without making any assumptions. In particular, we show how to extract the greatest possible amount of energy from a passive but not necessarily controllable system (e.g., a passive electric circuit) using state feedback. A complete characterisation of the set of solutions to the linear matrix inequalities in the positive-real and bounded-real lemmas is also obtained. In addition, we obtain necessary and sufficient conditions for a system to be non-expansive that augment the bounded-real condition with new conditions relevant to uncontrollable systems

Behavioral realizations using companion matrices and the smith form

Classical procedures for the realization of transfer functions are unable to represent uncontrollable behaviors. In this paper, we use companion matrices and the Smith form to derive explicit observable realizations for a general (not necessarily controllable) linear time-invariant be- havior. We then exploit the properties of companion matrices to efficiently compute trajectories, and the solutions to Lyapunov equations, for the realizations obtained. The results are motivated by the important role played by uncontrollable behaviors in the context of physical systems such as passive electrical and mechanical networks