A transformation for stability analysis of linear delay systems†

Sufficient conditions for stability and asymptotic stability on a half-open time interval are derived for linear time varying dynamic systems with delay. The derivation utilizes a linear, finite dimensional, time dependent transformation. Three examples show how the new results can bo used to determine stability properties of the original system from those of the transformed system.     

Stabilization of a class of linear time-delay systems†

Sufficient conditions for memoryless feedback stabilization of linear time-invariant delay systems are derived. Conditions for this class of system to be stabilized with any desired stability degree are also determined.     

Stable sampled-data feedback control of dynamic systems with time delays

Conditions for asymptotic stability of linear systems with time varying delays are obtained by specific application of a comparison method. The conditions are used to design stable sampled-data feedback controllers for linear systems governed by time invariant differential-difference equations.     

Stability of time-delay systems with sampled feedback†

Implementation of a feedback control which approximates the optimal control for a linear delay system is considered. Sufficient conditions for asymptotic stability of the resulting sampled-data feedback system are determined.     

Optimal discrete-time feedback control of mixed distributed and lumped parameter systems

The problem of designing an optimal discrete-time feedback controller is discussed for a linear system governed by coupled partial and ordinary differential equations. For the case of spatially concentrated controls and a quadratic performance index, the minimum cost and the optimal discrete-time controls are determined. Evaluation of computational requirements demonstrate the applicability to on-line computer control.