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Reachability and observability of linear systems over max-plus

Michael J. Gazarik, Edward W. Kamen (1999)

Kybernetika

This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable...

Reachability of cone fractional continuous-time linear systems

Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.

Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping

Alexander Y. Khapalov (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We show that the set of nonnegative equilibrium-like states, namely, like ( y d , 0 ) of the semilinear vibrating string that can be reached from any non-zero initial state ( y 0 , y 1 ) ∈ H 0 1 ( 0 , 1 ) × L 2 ( 0 , 1 ) , by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace L 2 ( 0 , 1 ) × { 0 } of L 2 ( 0 , 1 ) × H - 1 ( 0 , 1 ) . Our main results deal with nonlinear terms which admit at most the linear growth at infinity in y and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.

Reaching phase elimination in variable structure control of the third order system with state constraints

Andrzej Bartoszewicz, A. Nowacka (2006)

Kybernetika

In this paper the design of a time varying switching plane for the sliding mode control of the third order system subject to the velocity and acceleration constraints is considered. Initially the plane passes through the system representative point in the error state space and then it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops and remains motionless. The plane parameters (determining angles of inclination and the velocity of its motion) are...

Realizability of precompensators in linear multivariable systems: A structural approach

Javier Ruiz, Eduardo Castañeda (2014)

Kybernetika

In this work, given a linear multivariable system, the problem of static state feedback realization of dynamic compensators is considered. Necessary and sufficient conditions for the existence of a static state feedback that realizes the dynamic compensator (square or full column rank compensator) are stated in structural terms, i. e., in terms of the zero-pole structure of the compensator, and the eigenvalues and the row image of the controllability matrix of the compensated system. Based on these...

Realization of multivariable nonlinear systems via the approaches of differential forms and differential algebra

Jiangfeng Zhang, Claude H. Moog, Xiao Hua Xia (2010)

Kybernetika

In this paper differential forms and differential algebra are applied to give a new definition of realization for multivariable nonlinear systems consistent with the linear realization theory. Criteria for the existence of realization and the definition of minimal realization are presented. The relations of minimal realization and accessibility and finally the computation of realizations are also discussed in this paper.

Realization of nonlinear input-output equations in controller canonical form

Arvo Kaldmäe, Ülle Kotta (2018)

Kybernetika

In this paper necessary and sufficient conditions are given which guarantee that there exists a realization of a set of nonlinear higher order differential input-output equations in the controller canonical form. Two cases are studied, corresponding respectively to linear and nonlinear output functions. The conditions are formulated in terms of certain sequence of vector spaces of differential 1-forms. The proofs suggest how to construct the transformations, necessary to obtain the specific state...

Realization problem for a class of positive continuous-time systems with delays

Tadeusz Kaczorek (2005)

International Journal of Applied Mathematics and Computer Science

The realization problem for a class of positive, continuous-time linear SISO systems with one delay is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for the computation of positive minimal realizations is presented and illustrated by an example.

Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs

Tadeusz Kaczorek (2006)

International Journal of Applied Mathematics and Computer Science

The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.

Realization theory for linear and bilinear switched systems: A formal power series approach

Mihály Petreczky (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The paper represents the first part of a series of papers on realization theory of switched systems. Part I presents realization theory of linear switched systems, Part II presents realization theory of bilinear switched systems. More precisely, in Part I necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a linear switched system and a characterization of minimal realizations is presented. The paper treats two types of switched systems. The...

Realization theory for linear and bilinear switched systems: A formal power series approach

Mihály Petreczky (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal...

Realization theory for linear and bilinear switched systems: A formal power series approach

Mihály Petreczky (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal...

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