A classification of generalised state space reduction methods for linear multivariable systems
A functorial approach to the behaviour of multidimensional control systems
We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.
A further investigation for Egoroff's theorem with respect to monotone set functions
In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.
A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems
The notion of controlled invariance under quasi-static state feedback for discrete-time nonlinear systems has been recently introduced and shown to provide a geometric solution to the dynamic disturbance decoupling problem (DDDP). However, the proof relies heavily on the inversion (structure) algorithm. This paper presents an intrinsic, algorithm-independent, proof of the solvability conditions to the DDDP.
A necessary and sufficient condition for normality of linear control system with delays
A pencil approach to high gain feedback and generalized state space systems
A polynomial solution to regulation and tracking. I. Deterministic problem
A single-degree-of-freedom polynomial solution to the optimal feedback/feedforward stochastic tracking problem
Additional signals in linear discrete-time control systems. I. Additional control signal
Additionals signals in linear discrete-time control systems. II. Additional feedback signal
Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems
This paper presents a constrained decomposition methodology with output injection to obtain decoupled partial models. Measured process outputs and decoupled partial model outputs are used to generate structured residuals for Fault Detection and Isolation (FDI). An algebraic framework is chosen to describe the decomposition method. The constraints of the decomposition ensure that the resulting partial model is decoupled from a given subset of inputs. Set theoretical notions are used to describe the...
Algebraic systems theory towards stabilization under parametrical and degree changes in the polynomial matrices of linear mathematical models.
This paper deals with the stabilization of the linear time-invariant finite dimensional control problem specified by the following linear spaces and subspaces on C: χ (state space) = χ* ⊕ χd, U (input space) = U1 ⊕ U2, Y (output space) = Y1 + Y2, together with the linear mappings: Qs = χ x U x [0,t} --> χ associated with the evolution equation of the C0-semigroup S(t) generated by the matrices, of real and complex entries A belonging to L(χ,χ) and B belonging to L(U,χ) of a given differential...
Algebraic theory of discrete optimal control for multivariable systems [III.]
Algebraic theory of discrete optimal control for multivariable systems [II.]
Algebraic theory of discrete optimal control for multivariable systems [I.]
Alternate checking criteria for reachable controllability of rectangular descriptor systems
Contrary to state space systems, there are different notions of controllability for linear time invariant descriptor systems due to the non smooth inputs and inconsistent initial conditions. A comprehensive study of different notions of controllability for linear descriptor systems is performed. Also, it is proved that reachable controllability for general linear time invariant descriptor system is equivalent to the controllability of some matrix pair under an assumption milder than impulse controllability....
An algebraic approach to the synthesis of control for linear discrete meromorphic systems
An algebraic framework for linear identification
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
An algebraic framework for linear identification
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
An algebraic theory of order
In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified)...