Mlj Malo Hautus

Strong detectability and observers

Conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state. The concepts of strong detectability and strong observability, introduced before in the literature for discrete-time systems only, are defined and studied for continuous-time systems. It is shown that there are two different concepts of strong detectability, which coincide for discrete-time systems. Algebraic conditions for either concept are given. It is shown that these concepts are intimately related to the existence of strong observers, i.e. observers that only use the output of the plant.

System structure and singular control

The general continuous-time linear-quadratic control problem is considered. It is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem.

Linear feedback decoupling--Transfer function analysis

The problem of linear system decoupling is examined based on recent results on linear feedback. New insight is obtained, through which resolution of the decoupliug problem is accomplished by calculations, performed directly on the given transfer matrix. Computation of the decoupling compensators follows by easy constructions. The problem of feedback block decoupling with internal stability, is also formulated and resolved.

The output-stabilizable subspace and linear optimal control

The output-stabilizable subspace and linear optimal control A.H. W. Geerts & M.L.J. Hautus Properties of a certain subspace are linked to well-known problems in system theory.

Realization algorithms for systems over a principal ideal domain

In this paper realization algorithms for systems over a principal ideal domain are described. This is done using the Smith form or a modified Hermite form for matrices over a principal ideal domain. It is shown that Hos algorithm and an algorithm due to Zeiger can be generalized to the ring case. Also a recursive realization algorithm, including some results concerning the partial realization problem, is presented. Applications to systems over the integers, delay differential systems and two-dimensional systems are discussed.

Input regularity of cascaded systems

Necessary and sufficient conditions for the input regularity of a tandem connection of two multivariable systems are given. The results are specialized to the case of state-space equations, in which case input regularity is equivalent to controllability. Also the problem is considered whether the composite system can be made input regular by means of a suitable connection of the two subsystems.

A simple proof of Heymann's lemma

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Controllability and stabilizability of sampled systems

A definition of a general type of sampling mechanism at the input and the output of a continuous-time system is given. The coefficients of the resulting discrete-time system are computed and conditions for controllability and stabilizability are derived. Also, the problem is considered whether the system can be made controllable by a suitable linear connection of the sampling mechanism and the continuous-time system. Finally, it is shown that if the continuous-time system is controllable and an arbitrary sampling time is given, then a sampling mechanism can be constructed such that the sampled system is controllable. Similar results are obtained with stabilizability instead of controllability.

Linear-Quadratic Problems and the Riccati Equation

Linear-Quadratic (LQ) control problems have been investigated intensively since the fundamental and seminal paper of R.E. Kalman in 1960 ([KA]). In that paper, it was shown that the Riccati Equation plays an important role for the LQ-Problem. It is the purpose of the present paper to give an overview of the results relating the Riccati Equation with the LQ-Problem. LQ problems are also treated using the Hamiltonian matrix instead of the Riccati Equation. This will not be discussed in this paper. Neither will we deal with the use of Riccati equations outside of the LQ-problem context, e.g. in differential games and the H∞-optimization problem.

Digital Linear Control Theory Applied To Automatic Stepsize Control In Electrical Circuit Simulation

Adaptive stepsize control is used to control the local errors of the numerical solution. For optimization purposes smoother stepsize controllers are wanted, such that the errors and stepsizes also behave smoothly. We consider approaches from digital linear control theory applied to multistep BDF-methods.