Continuous-discrete Linear Systems Research Articles

On the admissibility and robust stabilization of 2D singular continuous–discrete linear systems

On the admissibility and robust stabilization of 2D singular continuous–discrete linear systems

Influence of Discretization Step on Asymptotic Stability of a Certain Class of Two-dimensional Continuous-discrete Fractional Linear Systems

Influence of Discretization Step on Asymptotic Stability of a Certain Class of Two-dimensional Continuous-discrete Fractional Linear Systems

Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs

AbstractA new formulation of the minimum energy control problem for the positive 2D continuous-discrete linear systems with bounded inputs is proposed. Necessary and sufficient conditions for the reachability of the systems are established. Conditions for the existence of the solution to the minimum energy control problem and a procedure for computation of an input minimizing the given performance index are given. Effectiveness of the procedure is demonstrated on numerical example.

Minimum Energy Control of 2D Positive Continuous-Discrete Linear Systems

Abstract The minimum energy control problem for the 2D positive continuous-discrete linear systems is formulated and solved. Necessary and sufficient conditions for the reachability at the point of the systems are given. Sufficient conditions for the existence of solution to the problem are established. It is shown that if the system is reachable then there exists an optimal input that steers the state from zero boundary conditions to given final state and minimizing the performance index for only one step (q = 1). A procedure for solving of the problem is proposed and illustrated by a numerical example.

Formula omitted]∞ filtering for time-invariant continuous–discrete linear systems

This paper discusses analysis and synthesis technique of H∞ filtering for time-invariant continuous–discrete linear systems which are composed of continuous systems, discrete systems, and their interconnections. Based on the bounded real lemma, Lyapunov stability conditions and H∞ constraints are formulated by linear matrix inequalities. Assuming that the eigenvalues of the systems are in a special region, it will be shown that an analytic H∞ design can be achieved and numerical methods to solve convex optimization problems are feasible in the continuous–discrete linear systems.

Positive realizations with reduced numbers of delays for 2D continuous-discrete linear systems

Abstract A new method is proposed for determination of positive realizations with reduced numbers of delays of linear 2D continuousdiscrete systems. Sufficient conditions for the existence of the positive realizations of a given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with a greater dimension. The proposed method is demonstrated on a numerical example.

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systemsAsymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

Positive fractional 2D continuous-discrete linear systems

Positive fractional 2D continuous-discrete linear systemsA new class of positive fractional 2D continuous-discrete linear systems is introduced. The solution to the equations describing by the new class of systems is derived. Necessary and sufficient conditions for the positivity of the fractional 2D continuous-discrete linear systems are established.

Stability of continuous-discrete linear systems described by the general model

Stability of continuous-discrete linear systems described by the general modelNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete linear systems described by the general 2D model are established. A procedure for checking the asymptotic stability is proposed. The effectiveness of the procedure is demonstrated on examples.

Stability of continuous-discrete linear systems with delays in state vector

Stability of continuous-discrete linear systems with delays in state vector A new class of positive continuous-discrete linear systems with delays in state vector described by the model based on 2D general model is addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of this class of linear systems are established. A procedure for checking the asymptotic stability is proposed. The effectiveness of the procedure is demonstrated on a numerical example.

Distributed receding horizon filtering for mixed continuous–discrete multisensor linear stochastic systems

A new distributed receding horizon filtering algorithm for mixed continuous–discrete linear systems with different types of observations is proposed. The distributed fusion filter is formed by summation of the local receding horizon Kalman filters (LRHKFs) with matrix weights depending only on time instants. The proposed distributed filter has a parallel structure and allows parallel processing of measurements; thereby, it is more reliable than the centralized version if some sensors become faulty. Also, the selection of the receding horizon strategy makes the proposed distributed filter robust against dynamic model uncertainties. The key contribution of this paper is the derivation of the error cross-covariance equations between the LRHKFs in order to compute the optimal matrix weights. High accuracy and efficiency of the proposed distributed filter are demonstrated on the damper harmonic oscillator motion and the water tank mixing system.

Robust stability of the new general 2D model of a class of continuous-discrete linear systems

The problems of asymptotic stability and robust stability of the new general 2D model of scalar linear dynamic continuous-discrete systems, standard and positive, are considered. Simple analytic conditions for asymptotic stability and for robust stability are given. These conditions are expressed in terms of coefficients of the model. The considerations are illustrated by numerical examples. The methods proposed can be generalized to scalar Fornasini-Marchesini and Roesser models of 2D continuous-discrete systems.

A low-complexity suboptimal filter for continuous–discrete linear systems with parametric uncertainties

We present a novel suboptimal filtering algorithm addressing estimation problems that arise in mixed continuous–discrete linear time-varying systems with stochastic parametric uncertainties. The suboptimal state estimate is formed by summing of local Kalman estimates with weights depending only on time instants t k . In contrast to optimal weights, the suboptimal weights do not depend on current measurements, and thus the proposed filter is of a low-complexity and it can easily be implemented in real-time. High accuracy and efficiency of the suboptimal filter are demonstrated on the damper harmonic oscillator motion and the vehicle motion constrained to a plane.

LMI-BASED ANALYSIS FOR CONTINUOUS-DISCRETE LINEAR SHIFT-INVARIANT nD SYSTEMS

In this paper, we describe the Linear Matrix Inequality (LMI) approach to the analysis and the synthesis of continuous-discrete linear shift-invariant multidimensional systems presented in the Roesser form. We consider stability, stability margins, robust stability, stabilization and stabilization to the prescribed stability margins and robust stabilization. An example is included as illustrations of the obtained results.

Control theory for a class of 2D continuous-discrete linear systems

This paper considers a general class of 2D continuous-discrete linear systems of both systems theoretic and applications interest. The focus is on the development of a comprehensive control systems theory for members of this class in a unified manner based on analysis in an appropriate algebraic and operator setting. In particular, important new results are developed on stability, controllability, stabilization and optimal control.

Stability and control of differential linear repetitive processes using an LMI setting

This paper considers differential linear repetitive processes which are a distinct class of two-dimensional continuous-discrete linear systems of both physical and systems theoretic interest. The substantial new results are on the application of linear-matrix-inequality-based tools to stability analysis and controller design for these processes, where the class of control laws used has a well defined physical basis. It is also shown that these tools extend naturally to cases when there is uncertainty in the state-space model of the underlying dynamics.

Kronecker product based stability tests and performance bounds for a class of 2D continuous–discrete linear systems

This paper reports further development of the so-called 1D Lyapunov equation based approach to the stability analysis of differential linear repetitive processes which are a distinct class of 2D continuous–discrete linear systems of both practical and theoretical interest. In particular, it is shown that this approach leads to stability tests which can be implemented by computations with matrices which have constant entries. Also if the example under consideration is stable then physically meaningful information concerning one key aspect of transient performance is available for no extra cost.

Stability conditions for a class of 2D continuous-discrete linear systems with dynamic boundary conditions

Repetitive processes are a distinct class of 2D systems of both practical and theoretical interest. Their essential characteristic is repeated sweeps, termed passes, through a set of dynamics defined over a finite duration with explicit interaction between the outputs, or pass profiles, produced as the process evolves. Experience has shown that these processes cannot be studied/controlled by direct application of existing theory (in all but a few very restrictive special cases). This fact, and the growing list of applications areas, has prompted an on-going research programme into the development of a 'mature' systems theory for these processes for onward translation into reliable generally applicable controller design algorithms. This paper develops stability tests for a sub-class of so-called differential linear repetitive processes in the presence of a general set of initial conditions, where it is known that the structure of these conditions is critical to their stability properties.

Stability analysis for a class of 2D continuous–discrete linear systems with dynamic boundary conditions

Differential linear repetitive processes are a class of continuous–discrete 2D linear systems of both practical and algorithmic interest. This paper undertakes a stability analysis for these processes in the presence of a general set of boundary conditions. The major conclusion is that a correct characterization of stability for these processes is critically dependent on the structure of these conditions.

Higher order discretisation methods for a class of 2-D continuous-discrete linear systems

Differential linear repetitive processes are a distinct class of two-dimensional linear systems which can be used, for example, to model industrial processes such as long-wall coal cutting operations. Also, they can be used to study key properties of classes of linear iterative learning schemes. The key feature of interest in the paper is the fact that information propagation in one of the two separate directions in such processes evolves continuously over a finite fixed duration and in the other direction it is, in effect, discrete. The paper develops discrete approximations for the dynamics of these processes and examines the effects of the approximation techniques used on two key systems-related properties. These are stability and the structure of the resulting discrete state-space models. Some ongoing work and areas for further development are also briefly noted.