Pole placement for generalized MFD's
Poles and zeroes of nonlinear control systems
During the last ten years, the concepts of “poles” and “zeros” for linear control systems have been revisited by using modern commutative algebra and module theory as a powerful substitute for the theory of polynomial matrices. Very recently, these concepts have been extended to multidimensional linear control systems with constant coefficients. Our purpose is to use the methods of “algebraic analysis” in order to extend these concepts to the variable coefficients case and, as a byproduct, to the...
Polynomial approach to conversion between Laplace and transforms
Polynomial approach to pole placement in MIMO systems
Polynomial Control Systems.
Polynomial controller design based on flatness
By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Polynomial controllers for finite-dimensional linear systems can then be designed with very natural choices for high level parameters design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.
Polynomial design of deadbeat control laws
Polynomial matrix solution to the discrete fixed-LAG smoothing problem
Polynomial systems theory applied to the analysis and design of multidimensional systems
The use of a principal ideal domain structure for the analysis and design of multidimensional systems is discussed. As a first step it is shown that a lattice structure can be introduced for IO-relations generated by polynomial matrices in a signal space X (an Abelian group). It is assumed that the matrices take values in a polynomial ring F[p] where F is a field such that F[p] is a commutative subring of the ring of endomorphisms of X. After that it is analysed when a given F[p] acting on X can...
Positive 2D discrete-time linear Lyapunov systems
Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
Positive and negative approximate controllability results for semilinear parabolic equations.
Positive and Negative Feedback in Engineering and Biology
No other concepts have shaken so deeply the bases of engineering like those of positive and negative feedback. They have played a most prominent role in engineering since the beginning of the previous century. The birth certificate of positive feedback can be traced back to a pair of patents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is already lost in time. We present in this paper a short review on the feedback's origins in the fields of engineering and biology....
Positive partial realization problem for linear discrete-time systems
A partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.
Positive stable realizations of fractional continuous-time linear systems
Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
Positive unknown inputs functional observers new design for positive linear systems
This paper deals with the problem of designing positive functional observers for positive linear systems subject to unknown inputs. The order of the designed observer is equal to the dimension of the functional to be estimated. The designed functional observer is always nonnegative at any time and converges asymptotically to the real functional state vector. In fact, we propose a new positive reduced order observer for positive linear systems affected by unknown inputs. The proposed procedure is...
Positivity and stability of fractional descriptor time-varying discrete-time linear systems
The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor timevarying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.
Positivity and stabilization of 2D linear systems
The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.
Positivity and stabilization of fractional 2D linear systems described by the Roesser model
A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation...
Powerful nonlinear observer associated with field-oriented control of an induction motor
In this paper, we associate field-oriented control with a powerful nonlinear robust flux observer for an induction motor to show the improvement made by this observer compared with the open-loop and classical estimator used in this type of control. We implement this design strategy through an extension of a special class of nonlinear multivariable systems satisfying some regularity assumptions. We show by an extensive study that this observer is completely satisfactory at low and nominal speeds...
Predictability and control synthesis
Processes modeled by a timed event graph may be represented by a linear model in dioïd algebra. The aim of this paper is to make temporal control synthesis when state vector is unknown. This information loss is compensated by the use of a simple model, the “ARMA” equations, which enables to introduce the concept of predictability. The comparison of the predictable output trajectory with the desired output determines the reachability of the objective.