Certain Algebraic Test for Analyzing Aperiodic Stability of Two-Dimensional Linear Discrete Systems

This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.

On necessity proof of strict bounded real lemma for generalized linear systems with finite discrete jumps

Some preliminary results on strict bounded real lemma for time-varying continuous linear systems are proposed, where uncertainty in initial conditions, terminal cost and extreme of the cost function are dealt with explicitly. Based on these results, a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.

A Modified Stability Analysis of Two-Dimensional Linear Time Invariant Discrete Systems within the Unity-Shifted Unit Circle

This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.

Output regulation problem for discrete-time linear time-delay systems by output feedback control

In this paper, we study the output regulation problem of discrete linear time-delay systems by output feedback control. We have established some results parallel to those for the output regulation problem of continuous linear time-delay systems.

Stability analysis for discrete linear systems with state saturation by a saturation-dependent Lyapunov functional

This paper concerns the stability analysis problem of discrete linear systems with state saturation using a saturation-dependent Lyapunov functional. We introduce a free matrix characterized by the sum of the absolute value of each elements for each row less than 1, which makes the state with saturation constraint reside in a convex polyhedron. A saturation-dependent Lyapunov functional is then designed to obtain a sufficient condition for such systems to be globally asymptotically stable. Based on this stability criterion, the state feedback control law synthesis problem is also studied. The obtained results are formulated in terms of bilinear matrix inequalities that can be solved by the presented iterative linear matrix ineoualitv algorithm. Two numerical examoles are used to demonstrate the effectiveness of the nronosed method_

A High-order Internal Model Based Iterative Learning Control Scheme for Discrete Linear Time-varying Systems

In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iterationvarying desired trajectories. A high-order internal model(HOIM) is utilized to describe the variation of desired trajectories in the iteration domain. In the sequel, the HOIM is incorporated into the design of learning gains. The learning convergence in the iteration axis can be guaranteed with rigorous proof. The simulation results with permanent magnet linear motors(PMLM) demonstrate that the proposed HOIM based approach yields good performance and achieves perfect tracking.

Robust Fault-tolerant Iterative Learning Control for Discrete Systems via Linear Repetitive Processes Theory

This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetitive processes is used to develop formulas for gain matrices design, together with convergent conditions in terms of linear matrix inequalities. An extension to deal with model uncertainty of the polytopic or norm bounded form is also developed and an illustrative example is given.