MB2 Linear Systems I: Theory

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Reachability and Controllability of 2D Positive Linear Systems with State Feedbacks

Authors:

Kaczorek T., Warsaw University of Technology, Poland

ABSTRACT

It is shown that the reachability and controllability of positive 2D linear systems are not invariant under the state-feedbacks. By suitable choice of the state-feedbacks the unreachable positive 2D Roesser model can be made reachable and the controllable positive 2D Roesser model can be made uncontrollable.

Key Words: reachability, controllability, positive 2D Roesser model, state-feedback.

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Anticipatory 1D and 2D linear systems

Authors:

Kaczorek T., Warsaw Technical University, Poland

ABSTRACT

Notions of anticipatory systems for discrete-time and continuous-time 1D linear systems and 2D discrete linear systems are introduced. A discrete-time system is called anticipatory if its state vector and output vector depend on the future values of inputs. A continuous-time system is called anticipatory if its state vector and output vector depend on the derivatives of inputs. Necessary and sufficient conditions for the anticipation of singular discrete-time and continuous-time 1-D linear systems are established. It is shown that the discrete-time system obtained by discretisation from continuous-time one is anticipatory for any value of the discretisation step if and only if the continuous-time system is anticipatory. Necessary and sufficient conditions for the anticipation of the singular 2D Roesser model are established.

Key Words. 1D and 2D anticipatory systems, Roesser model, dicretisation.

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A new approach to estimate controllable and recoverable regions for systems with state and control constraints

Authors:

Yfoulis A.C., UMIST, United Kingdom

Muir A., UMIST, United Kingdom

Wellstead E.P., UMIST, United Kingdom

ABSTRACT

In this paper the problem of estimating controllable and recoverable regions for classes of nonlinear systems in the presence of uncertainties, state and control constraints is considered. A new computational technique is proposed based upon a ray-gridding idea in contrast to the usual gridding techniques. The new technique is also based on the positive invariance principle and the use of Piecewise Linear (PL) Lyapunov functions to generate polytopic approximations to the controllable/recoverable region with arbitrary accuracy. Various types of stabilising controllers achieving certain trade-o s between robustness, performance and safety, while respecting state and control constraints, can be easily generated. The technique allows the approximation of nonlinear systems via piecewise linear uncertain models which reduces the conservatism associated with linear uncertain models.

Key Words. Controllable region, recoverable region, PL-Lyapunov functions.

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The reduced order Luenberger observer and its relation to the full-state observer

Authors:

Alexandridis A., University of Patras, Greece

ABSTRACT

Abstract – The relation between the reduced-order Luenberger and the full-order state observer is considered. In particular, it is proved that for a completely observable linear system, one can always design a full-order state observer which is dynamically equivalent to any arbitrarily selected reduced-order Luenberger observer.

Keywords – Observers, Linear systems, State estimation.

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Robust Gain and Phase Margins for Systems with Parametric Uncertainty

Authors:

Tan N., University of Sussex, United Kingdom

Kaya I., University of Sussex, United Kingdom

ABSTRACT

Gain and phase margins are two important frequency domain specifications which are widely used for controller design. In this paper, a procedure is given for computing the robust gain and phase margins of systems with an uncertain transfer function by using the 2q-convex parpolygonal value set of polynomials with affine linear uncertainty. An example is included to illustrate the benefit of the method presented.

Keywords: Uncertain systems; Nyquist envelope; Robust gain margin; Robust phase margin

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