Nutan Kumar Tomar

Full- and reduced-order observer design for rectangular descriptor systems with unknown inputs

Abstract In this paper, methods are proposed to design Luenberger type full- and reduced-order observers for rectangular descriptor systems with unknown inputs. These methods are based on the effect of pre- and post-multiplicative operation of a linear transformation, derived here by means of simple matrix theory. Sufficient conditions for the existence of observers are given and proved. Numerical examples are given to illustrate the effectiveness of the proposed method.

On Complete and Strong Controllability for Rectangular Descriptor Systems

Algebraic criteria have been developed to check the complete and strong controllability for rectangular descriptor systems. Under the assumption of controllability at infinity, the complete controllability for a descriptor system has been proved to be equivalent to the controllability for a normal system. The essence of the technique to design the proposed normal system is based on the row and column compression operations of basic matrix theory. The strong controllability concept for a descriptor system is related with the complete controllability concept for another descriptor system. Examples are provided to illustrate the theory.

On observability of irregular descriptor systems

Abstract In this paper, a method is proposed to check the observability of irregular linear time invariant descriptor systems. The method is based on the properties of restricted system equivalent, derived here from a given descriptor system by means of simple matrix theory. Using restricted system equivalent form, equivalence between the observability of a given descriptor system and that of its corresponding normal system has been established.

Detectability and observer design for linear descriptor systems

In this paper, a method is proposed to design Luenberger type observer for a class of linear descriptor systems satisfying complete detectability condition. The method is based on the properties of restricted system equivalent, derived here from a given descriptor system by means of simple matrix theory. Using restricted system equivalent form, equivalence between the detectability of a given descriptor system and that of a normal system has been established. Coefficient matrices of the proposed observer have been synthesized using pole placement technique of normal system theory and LMI approach based on the Lyapunov stability theory.

Index reduction for rectangular descriptor systems via feedbacks

Index plays a fundamental role in the study of descriptor systems. For regular descriptor systems, calculation of the index can be performed by calculating the index of the nilpotent matrix obtained by means of the Weierstrass canonical form. Notwithstanding, if the system is not regular, there is no algebraic technique to determine the index of the system. A sufficient algebraic criterion is provided to determine the index of a general linear time-invariant descriptor systems. Thereafter, we provide an alternate but lucid proof of the fact that impulse controllability is necessary and sufficient for the existence of a semistate feedback such that the closed loop system is of the index at most one. Finally, a sufficient test for the existence of a semistate feedback such that the closed loop system is of the index at most two is provided. Examples are given to illustrate the presented theory.

Quadrature Filters for Underwater Passive Bearings-Only Target Tracking

A typical underwater passive bearings-only target tracking problem is solved using nonlinear filters namely cubature Kalman filter (CKF), Gauss-Hermite filter (GHF) and sparse-grid Gauss-Hermite filter (SGHF). The performance of the filters is compared in terms of estimation accuracy, track-loss count and computational time. Theoretical Cramer-Rao lower bound (CRLB) is used to determine the maximum achievable performance and to compare the error bounds of various filters used.

Ballistic target tracking and its interception using suboptimal filters on reentry

In this work, tracking of a ballistic target on reentry using an interceptor missile is studied where the main motive is to accurately estimate the acceleration of the incoming ballistic target. To achieve this, nonlinear filters like the unscented Kalman filter (UKF), cubature Kalman filter (CKF) and cubature quadrature Kalman filter (CQKF) are used. For a possible interception of the target by an interceptor, proportional navigation guidance (PNG) law has been used. Efficiency of the filtering techniques has been studied by plotting the root mean square error (RMSE) of the target acceleration and by calculating the final miss-distance.

Synchronization of Rössler chaotic system for secure communication via descriptor observer design approach

An observer construction method for semilinear descriptor systems of the form Eẋ = Ax + f, where E (singular), A are linear operators and f is a nonlinear function, is studied. Using a new approach, based on matrix theory, it is shown that an observer may be designed under certain conditions on system operators if one linear matrix inequality (LMI) is satisfied. By treating the transmitted signal as an extra state, chaotic Rössler system is rewritten in the semilinear descriptor system form and then using proposed observer the transmitted signal is retrieved. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.

Impulse controllability and impulse elimination in rectangular descriptor systems

In this paper, a decomposition of system matrices of linear time invariant rectangular descriptor systems is proposed. Using the decomposition, a technique is developed to check the impulse controllability for rectangular descriptor systems. Necessary and sufficient conditions are stated and proved to design a proportional plus derivative feedback such that the closed loop system is free of impulse. Examples are given to illustrate the presented theory.

Bearing-Only Tracking Using Sparse-Grid Gauss–Hermite Filter

In this paper, performance of sparse-grid Gauss–Hermite filter (SGHF) in bearings-only tracking (BOT) problem has been studied and compared with the performance of unscented Kalman filter (UKF), cubature Kalman filter (CKF), and Gauss–Hermite filter (GHF). The performance has been compared in terms of estimation accuracy and percentage of track loss, subjected to high initial uncertainty. It has been found that track loss of SGHF is less than all other quadrature filters with comparable estimation accuracy.