Victor Sreeram

Controlling Chaos in a Memristor Based Circuit Using a Twin-T Notch Filter

After the successful solid state implementation of memristors, a lot of attention has been drawn to the study of memristor based chaotic circuits. In this paper, a systematic study of chaotic behavior in such system is performed with the help of nonlinear tools such as bifurcation diagrams, power spectrum analysis, and Lyapunov exponents. In particular, a Twin-T notch filter feedback controller is designed and employed to control the chaotic behavior in the memristor based chaotic circuit. Both simulation and experiment results validate the proposed control method.

Hyperchaos in a memristor-based modified canonical Chua's circuit

After the successful solid state implementation of the memristor, memristor-based circuits have received a lot of attention. In this paper, a memristor with cubic nonlinear characteristics is employed in the modified canonical Chuas circuit. A systematic study of hyperchaotic behavior in this circuit is performed with the help of nonlinear tools such as Lyapunov exponents, phase portraits and bifurcation diagrams. In particular, an imitative memristor circuit is examined to reveal the construction of hyperchaotic attractors.

Model reduction for state-space symmetric systems

In this paper, the model reduction problem for state-space symmetric systems is investigated. First, it is shown that several model reduction methods, such as balanced truncation, balanced truncation which preserves the DC gain, optimal and suboptimal Hankel norm approximations, inherit the state-space symmetric property. Furthermore, for single input and single output (SISO) state-space symmetric systems, we prove that the H∞ norm of its transfer functions can be calculated via two simple formulas. Moreover, the SISO state-space symmetric systems are equivalent to systems with zeros interlacing the poles (ZIP) under mild conditions.

Optimal simultaneous stabilization of linear single-input systems via linear state feedback control

Simultaneous stabilization of a collection of linear time-invariant systems is considered. The aim is to develop a practical method for the design of a single feedback controller such that all the systems involved are stabilized with good transient responses. Hurwitzs necessary and sufficient conditions are used as the required set of constraints for simultaneous stability. For transient behaviour, we introduce the usual quadratic objective function as performance index for each system. Their sum is the objective function for the collection of systems and the problem is to minimize it by choosing a feedback gain vector subject to boundedness and the Hurwitz stability constraints. A computational technique is proposed for solving this problem. The results obtained give good transient behaviour. For illustration, two numerical examples are solved.

Model reduction of linear discrete systems via weighted impulse response gramians

Abstract A new method for model reduction of linear discrete systems is proposed. It is based on the weighted impulse response gramians proposed here for discrete systems. These gramians are extensions of the ones proposed for linear continuous systems (Agathoklis and Sreeram 1988 a, 1990) and contain information on the input-output behaviour of the system. The reduced-order models are obtained by retaining the states corresponding to the dominant eigenvalues of these gramians and are stable if the original system is stable. The method is illustrated by a numerical example and is compared with well-known model reduction techniques

A Survey/Review of Frequency-Weighted Balanced Model Reduction Techniques

In this paper, a survey/review of frequency-weighted balanced model reduction techniques is presented. Several comments regarding their properties are given. A modified frequency interval Gramian based method is also presented. The computational issues are also discussed. The techniques are illustrated and compared using practical numerical examples.

Existence conditions for unknown input functional observers

This article presents necessary and sufficient conditions for the existence and design of an unknown input Functional observer. The existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions. The existence of the observer does not require the satisfaction of the observer matching condition (i.e. Equation (16) in Hou and Muller 1992, ‘Design of Observers for Linear Systems with Unknown Inputs’, IEEE Transactions on Automatic Control, 37, 871–875), is not limited to estimating scalar functionals and allows for arbitrary pole placement. The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.

H∞ control for discrete-time singularly perturbed systems with two Markov processes

Abstract This paper discusses the H ∞ state feedback control problem for discrete-time Markovian jump singularly perturbed systems whose singularly perturbation parameters belong to another Markov process. Firstly, new mean-square exponential stability condition with H ∞ performance for discrete-time singularly perturbed systems with two Markov processes is given in terms of linear matrix inequalities (LMIs) with equality constraints via a novel method. Then, based on the derived stability condition where e is involved, however, an H ∞ controller which is independent of e is constructed. An effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the H ∞ controller solutions. Finally, illustrative examples are presented to show the benefits and validity of the proposed approaches.

Model Reduction Via Limited Frequency Interval Gramians

An improved frequency domain interval Gramian-based model reduction scheme for discrete time systems is presented. It is first shown that two of the main results presented in the model reduction method of are incorrect. Improved methods which overcomes these shortcomings are then presented. Improved methods not only yields stable reduced-order models but also have easily computable frequency response error bounds. The method is further extended to 2-D separable denominator system approximation. The simulation results show the effectiveness of the proposed scheme.

Identification and model reduction from impulse response data

Two new algorithms for identification and model reduction of stable linear continuous systems are proposed, based on the weighted impulse response gramians (Agathoklis and Sreeram 1988 b). In identification, the model parameters are obtained from the solution of a linear system of equations with coefficients obtained from the numerical evaluation of the weighted impulse response gramians. The reduction technique is based on retaining part of the original weighted impulse response gramians obtained as the solutions to the Lyapunov equation for the original system in controllability canonical form. This yields different stable models for different values of the weighting factor. The model corresponding to zero weighting factor matches the impulse response norm of the original system and its derivatives exactly. Finally, the method is illustrated by a numerical example and is compared with well-known balanced realization techniques.