Repetitive control that asymptotically tracks or rejects periodic signals has been widely used in many applications. For linear time invariant system, this problem has been thoroughly studied and solved. This paper presents the analysis and synthesis of repetitive control algorithms to track or reject periodic signals for linear time varying systems. Both continuous and discrete time domain res...

We consider triples of matrices (E,A, B), representing singular linear time invariant systems in the form Eẋ(t) = Ax(t) + Bu(t), with E, A ∈ Mp×n(C) and B ∈ Mn×m(C), under proportional and derivative feedback. Using geometrical techniques we obtain miniversal deformations that permit us to study sensivity and structural stability of singular systems. Key-Words:Singular linear systems, proportio...

In this paper we define strong and weak common quadratic Lyapunov functions (CQLF’s) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the non-existence of a strong CQLF, for a pair of LTI systems, is characterised by easily verifiable algebraic conditions. These conditions are found to play an important role in provin...

Both linear time-invariant (LTI) and linear time-varying (LTV) systems are addressed. They are placed in a unified conceptual framework. The characteristic equation for each subclass is formulated as a Riccati equation. Where LTI-systems lead to algebraic Riccati equations, the LTV-case generalizes this result to differential Riccati equations.

This paper presents a survey on the recent contributions to linear time-invariant delaydifferential systems in the behavioral approach. In this survey both systems with commensurate and with incommensurate delays will be considered. The emphasis lies on the investigation of the relationship between various systems descriptions. While this can be understood in a completely algebraic setting for ...

In this paper a design methodology is proposed to provide a constructive solution to the problem of designing a full order observer for linear time invariant systems subjected to unknown disturbances. Necessary conditions for existence of unknown input observers are stated and solved using generalized matrix inverse. The effect of unknown disturbance present in the system is eliminated from the...

Unitary similarity transformations furnish a powerful vehicle for generating innnite generic classes of signal analysis and processing tools based on concepts diierent from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation , performing standard processing techniques on the transformed signal, and then (in some case...

For the first time, in this paper, a stability test procedure is proposed for linear time-invariant fractional order systems (LTI FOS). Paper extends some basic results from the area of finite time and practical stability to linear, continuous, fractional order time invariant time-delay systems given in state space form. Sufficient conditions of this kind of stability, for particular class of f...

This paper studies the controllability and observability of discrete-time systems with network-induced variable delays. Since controllability and observability are structural properties of systems, which are first checked before control design, we study if a controllable (resp. observable) non-delayed system can loose these properties if we augment the model with particular pure input-output va...

This paper attempts to give a thorough treatment of the performance limitation of a linear time invariant multivariable system in tracking a reference signal which is a linear combination of a step signal and several sinusoids with different frequencies. The tracking performance is measured by an integral square error between the output of the plant and the reference signal. Our purpose is to f...