Wojciech Paszke

Robust stability and stabilisation of 2D discrete state-delayed systems

Abstract In this paper, we first present sufficient stability and robust stability conditions for discrete linear state-delayed 2D systems in terms of linear matrix inequalities. All results are obtained with Fornasini–Marchesini delay model but appropriate transformation to the corresponding Roesser form is provided as well. Generalisation to the multiple state-delayed case is also given. Then the stabilisation and robust stabilisation using static state feedback are studied. Stabilising feedback gain matrices are constructed based on the solutions of certain linear matrix inequalities. An numerical example is used to illustrate the effectiveness of the approach.

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.

Robust Filtering for Uncertain 2-D Continuous Systems

This paper considers the problem of robust H/sub /spl infin// filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H/sub /spl infin// norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H/sub /spl infin// filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.

Robust H/sub /spl infin// filtering for Uncertain2-D continuous systems

This paper considers the problem of robust H/sub /spl infin// filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H/sub /spl infin// norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H/sub /spl infin// filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.

Positive real control of two-dimensional systems: Roesser models and linear repetitive processes

This paper considers the problem of positive real control for two-dimensional (2-D) discrete systems described by the Roesser model and also discrete linear repetitive processes, which are another distinct sub-class of 2-D linear systems of both systems theoretic and applications interest. The purpose of this paper is to design a dynamic output feedback controller such that the resulting closed-loop system is asymptotically stable and the closed-loop system transfer function from the disturbance to the controlled output is extended strictly positive real. We first establish a version of positive realness for 2-D discrete systems described by the Roesser state space model, then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four LMIs. When these LMIs are feasible, an explicit parameterization of the desired output feedback controllers is given. We then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1-D state-space form. Finally, we provide numerical examples to demonstrate the applicability of the approach.

Guaranteed cost control of uncertain differential linear repetitive processes

This paper deals with the problem of designing a control law for differential linear repetitive processes based on minimizing a cost function in the presence of uncertainties in the process model. This control law results in a closed-loop stable process with an associated cost function which is bounded for all admissible uncertainties. Moreover, an optimization algorithm is developed to design this law such that it minimizes the upperbound of the closed-loop cost function.

Iterative Learning Control by Two-Dimensional System Theory applied to a Motion System

For systems that repeatedly perform a given task, iterative learning control (ILC) makes it possible to update the control signal to the system during successive trials in order to improve the tracking performance. Iterative learning control has an inherent 2-D system structure since there are two independent variables, i.e. time and trials. In this paper, the 2-D structure is exploited in a method that yields in a one step synthesis both a stabilizing feedback controller in the time domain and an ILC controller, which guarantees convergence in the trial domain. A norm-bounded uncertainty model is added to guarantee a robust controller performance. The controller synthesis can be performed by means of linear matrix inequalities. The effectiveness of the theoretical results will be illustrated using a motion system.

H/sub /spl infin// control of differential linear repetitive processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or two-dimensional (2D) systems theory. Here, we give new results on the relatively open problem of the design of physically based control laws using an H/sub /spl infin// setting. These results are for the sub-class of so-called differential linear repetitive processes, which arise in application areas such as iterative learning control.

LMI based stability analysis and controller design for a class of 2D continuous-discrete linear systems

Differential linear repetitive processes are a distinct class of 2D continuous-discrete linear systems of both applications and systems theoretic interest. In the latter area, they arise, for example, in the analysis of both iterative learning control schemes and iterative algorithms for computing the solutions of nonlinear dynamic optimal control algorithms based on the maximum principle. Repetitive processes cannot be analysed/controlled by direct application of existing systems theory and to date there are few results on the specification and design of control schemes for them. The paper uses an LMI setting to develop the first really significant results in this problem domain.

KYP lemma based stability and control law design for differential linear repetitive processes with applications

Repetitive processes are a class of two-dimensional systems that have physical applications, including the design of iterative learning control laws where experimental validation results have been reported. This paper uses the Kalman–Yakubovich–Popov lemma to develop new stability tests for differential linear repetitive processes that are computationally less intensive than those currently available. These tests are then extended to allow control law design for stability and performance.