M. E. Sawan

Robust stability of singularly perturbed systems

The robust stability problem of linear time-invariant singularly perturbed systems is discussed, where the system matrix may have a parameter perturbation bounded by the Hα-norm. A sufficient condition for the upper bound of e is given, such that the stability of the actual system (or the full-order model) can be inferred from the analysis of the reduced-order system (or the slow model) in separate time scales.

The observer-based controller design of discrete-time singularly perturbed systems

A class of linear shift-invariant discrete-time singularly perturbed systems with inaccessible states is considered. A design technique is formulated by which the stabilizing controller can be formed through the controllers of the slow and fast subsystems. Sufficient conditions for stability of the closed-loop system under this composite controller are given.

Reduced order discrete-time models

Linear shift-invariant discrete-time systems satisfying the two time scale property-are considered. Conditions for a complete separation of slow and fast subsystems are given. Subsystem regulator problems are investigated and the controllability property of the system is established based on the subsystem controllability properties. A subsystem controller design method is proposed depending on the separability of the slow and fast controls.

A note on the discrete Lyapunov and Riccati matrix equations

Abstract Inequalities which are satisfied by the determinants of the positive definite solutions of the discrete algebraic Riccati and Lyapunov matrix equations are presented. The results give lower bounds for the product of the eigenvalues of the matrix solutions. Also for a discrete Lyapunov equation, an algorithm is presented to determine under what conditions a positive diagonal solution will exist. If all the conditions are satisfied, the algorithm also provides such a diagonal solution.

Joint Time Delay and Frequency Estimation Without Eigen-Decomposition

In this letter, we addressed the problem of estimating the time delay and the frequencies of noisy sinusoidal signals received at two spatially separated sensors. We employ the Propagator Method (PM) in conjunction with the well-known MUSIC/root-MUSIC algorithm; the proposed method would generate estimates of the unknown parameters. Such estimates are based on the observation and/or covariance matrices. Moreover, the PM does not require the eigenvalue decomposition (EVD) or singular value decomposition (SVD) of the cross-spectral matrix (CSM) of received signals; therefore, a significant improvement in computational load is achieved. Computer simulations are also included to demonstrate the effectiveness of the proposed method.

Decentralized control for two time-scale discrete-time systems

Output feedback design of discrete-time decentralized systems with slow and fast modes is considered. Conditions for the complete separation of slow and fast subsystems are given. The slow and fast subsystem outputs, which are obtained by applying the slow and fast subcontrollers to the corresponding subsystems, will be shown to approximate those of the original system. Also, the composite control, when being applied to the original system, will place the eigenvalues sufficiently close to the desired locations.

H ∞ model matching problem for singularly perturbed systems

Abstract The model matching problem for single-input single-output singularly perturbed systems is considered. Two sets of sufficient conditions are obtained to guarantee the existence of a two-frequency-scale solution: one for the optimal and one for a suboptimal case. Both the minimum-phase and the non-minumum-phase cases are treated. The sub-optimal two-frequency-scale solution constructed in this paper uses the solutions of two well-defined lower-order problems, and therefore it is numerically better conditioned and computationally less demanding than the traditional optimal methods. A two-stage algorithm for the computation of the suboptimal TFS solution is presented.

On the well-posedness of discrete-time systems with slow and fast modes

Linear shift-invariant discrete-time systems satisfying the two time-scale property are considered. Conditions for a complete separation of slow and fast subsystems are given. The composite controller will be formed from the slow and fast subsystem controllers. The slow and fast subsystem trajectories will be obtained and they will be shown to approximate those of the original system. Conditions for existence of the solutions of the subsystem regulator problems will also be given

Propagator Method for joint time delay and frequency estimation

A novel method of estimating the differential delay of a sinusoidal signal is considered. The new method utilizes the propagator method (PM) which does not require the eigen-decomposition of the cross-spectral matrix (CSM) in estimating the delay of a signal received at two separated sensors. Moreover, the proposed method would generate estimates of the signal frequencies. Such estimates of time delay and frequencies are based on the observation and/or covariance matrices. Computer simulation is performed to validate the new procedure.

Efficient Structure-Based Carrier Offset Estimator for OFDM System

In this paper, we proposed a closed form solution for blind Orthogonal Frequency Division Multiplexing (OFDM) Carrier Frequency Offset (CFO) estimation employing the Rank- Revealing QR triangular factorization Method (RRQR). The advantage of using the RRQR it gives precious information about numerical rank and efficiently separates the signal space from the noise space. Furthermore, the RRQR does not involve the eigenvalue decomposition (EVD) or singular value decomposition (SVD) of co-variance matrix of the received signals and is a valuable tool in linear algebra to meet compatibility requirement of real time environment. Computer simulations shows the superior performance and much less processing time of RRQR compared with the method employing ESPRIT Algorithm Index-Terms: OFDM, Carrier Frequency Offset, DFT, Estimation, RRQR Method.