Multiple-output Linear Time-invariant Systems Research Articles

High‐order sliding‐mode functional observers for multiple‐input multiple‐output (MIMO) linear time‐invariant systems with unknown inputs

AbstractFor arbitrary multiple‐input multiple‐output linear time invariant systems with unknown inputs this article provides sufficient conditions to estimate linear functionals of the state variables. When the unknown input is uniformly bounded these conditions are strictly weaker than the classical conditions for functional unknown input observers, well‐known in the literature, and generalize previous results using discontinuous differentiators. Furthermore, a general methodology is proposed to design functional observers, that are able to estimate the functionals, when possible, exactly and in finite‐time or fixed‐time. Instead of using a cascade of Luenberger observers and high‐order sliding‐mode differentiators, standard in the literature for this problem, a bi‐homogeneous observer of reduced order is proposed in the article. Proofs of the convergence are provided using smooth Lyapunov functions and an academic example illustrates the behavior of the proposed observer for a system not tractable with the available methods.

MIMO tracking control of LTI systems: A geometric approach

This paper addresses the tracking problem of constant references for multiple-input multiple-output linear time-invariant systems. We provide necessary and sufficient conditions for the solvability of the problem under the minimal set of assumptions that guarantee the well-posedness of every control problem requiring stability. Our approach allows to solve tracking problems for systems which are possibly nonright-invertible, simply (not asymptotically) stabilizable, and possibly with invariant zeros at the origin. Our methodology is constructive and results in the design of a stabilizing feedback matrix and a feedforward signal which solve the problem.

Substructure Preservation Sylvester-based Model Order Reduction with Application to Power Systems

A new substructure preservation Sylvester-based model order reduction technique with application to power systems is presented in this article. The new approach is intended for multiple-input–multiple-output linear time invariant systems, given in the form of state-space realization with the objective of obtaining a proper reduced-order model (complexity reduction), preserving the dominant eigenvalues of the full-order model as a subset in the reduced model, and maintaining a minimum steady-state error. The proposed reduction method is performed based on transforming the system state matrix into a special form, taking into account the dominant eigenvalues, while the rest of the model transformation is derived utilizing the Sylvester equation formula. Once the system is transformed, the reduced-order model is obtained by truncating the less dominant eigenvalues using the singular perturbation technique. To evaluate the potential of the new approach, results of the proposed technique are compared to some of the well-known methods for model order reduction and relatively recently published work. Results comparison shows the superiority of the new method especially in terms of time convergence.

Optimal tracking over noisy channels in the presence of data dropouts

This study investigates the optimal tracking performance of multiple-input multiple-output linear time-invariant systems over a noisy channel in the feedback path. The communication channel is also subject to data dropouts, which was modelled as a binary stochastic process. The problem under consideration amounts to determining the minimal error in tracking a Brownian motion random process, which emulates a step reference signal in the deterministic setting. With the unity feedback and two-parameter control structure, a lower bound and an exact expression of optimal tracking performance are obtained respectively. It is shown how the noise may degenerate the tracking performance and how the data dropouts effect may intertwine with unstable poles and non-minimum phase zeros, including the location and direction, which are intrinsic characteristics of the plant. Finally, computer simulations are provided to illustrate the analytical results obtained.

A Block-by-Block Blind Post-FFT Multistage Beamforming Algorithm for Multiuser OFDM Systems Based on Subcarrier Averaging

Chi et al. proposed a computationally efficient fast kurtosis maximization algorithm for blind equalization of multiple-input multiple-output linear time-invariant systems. This algorithm is also an iterative batch processing algorithm and has been applied to blind source separation. This paper considers blind beamforming of multiuser orthogonal frequency division multiplexing (OFDM) systems. Assuming that the channel is static within one OFDM block, a blind post-FFT multistage beamforming algorithm (MSBFA) based on subcarrier averaging is proposed. The algorithm basically comprises:( i) source (path signal) extraction using a hybrid beamforming algorithm composed of a Fourier beamformer and a kurtosis maximization beamformer, (ii) time delay estimation and compensation, (iii) classification (path-to-user association) and blind maximum ratio combining (of path signals). The designed beamformer is exactly the same for all the subcarriers, effectively utilizes multipath diversity for performance gain, and works well even in an environment with spatially correlated sources. Some simulation results are presented to demonstrate the effectiveness of the proposed MSBFA.

Wordlength Optimization of Linear Time-Invariant Systems With Multiple Outputs Using Geometric Programming

This paper proposes two new methods for optimizing hardware resources in finite wordlength implementation of multiple-output (MO) linear time-invariant (LTI) systems. The hardware complexity is measured by the exact internal wordlength used for each intermediate data. The first method relaxes the wordlength from integer to real-value and formulates the design problem as a geometric programming, from which an optimal solution of the relaxed problem can be determined. The second method is based on a discrete optimization method called the marginal analysis method, and it yields the desired wordlengths in integer values. By combining these two methods, a hybrid method is also proposed, which is found to be very effective for large scale MO LTI systems. To illustrate the effectiveness of the proposed methods, wordlength optimization problems of two-channel structural perfect reconstruction filter banks and multiplier-less fast Fourier transforms are studied in detail. Design results show that the proposed algorithms offer better results and a lower design complexity than conventional methods

Canonical state space representations for multivariable systems

Abstract The problem of state space representations for multiple-input, multiple-output linear time-invariant systems is considered. The known definitions of the first and second canonical forma for scalar systems are used to facilitate the derivation of explicit canonical expressions for multivariable systems.