Reza Mohajerpoor

Reduced-order functional observers with application to partial state estimation of linear systems with input-delays

Reduced-order multi-functional observer design for multi-input multi-output linear time-invariant (LTI) systems with constant delayed-inputs is studied. This research is useful in the input estimation of LTI systems with actuator delay, as well as system monitoring and fault detection of these systems. Two approaches for designing an asymptotically stable functional observer for the system are proposed: delay-dependent and delay-free. The delay-dependent observer is infinite-dimensional, while the delay-free structure is finite-dimensional. Moreover, since the delay-free observer does not require any information on the time delay, it is more practical in real applications. However, the delay-dependent observer contains less restrictive assumptions and covers more variety of systems. The proposed observer design schemes are novel, simple to implement, and have improved numerical features compared to some of the other available approaches to design (unknown-input) functional observers. In addition, the prop...

Partial state estimation: A new design approach

There are three different approaches for functional observer design for Linear Time-Invariant (LTI) systems within the literature. One of the most common methods has been proposed by Aldeen [1] and further developed by others. We found several examples in which the necessary and sufficient conditions for the existence of a functional observer are actually not sufficient for this methodology. This finding motivated us to develop a new methodology for designing functional observers. Our new method provides enough degrees of freedom for the observer design parameter and it improves the weakness within the Aldeens method in solving the observer coupled matrix equations. In this paper, we present the reason and an example to show the insufficiency of the former method. Furthermore, we present our new developed methodology. An illustrative algorithm also describes the design procedure step by step. A numerical example and simulation results support our findings and performance of the proposed method.

Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances

It is well-known that the stability analysis of time-delay systems is a key step to design appropriate controllers and/or filters for those systems. In this paper, the problem of the delay-dependent stability analysis of neutral systems with mixed interval time-varying delays with/without nonlinear perturbations is revisited. Bounded derivatives of the discrete and neutral delays with upper-bounds not limited to be strictly less than one are considered. New stability criteria are developed using the Lyapunov Krasovskii methodology which are expressed in terms of linear matrix inequalities (LMIs). An augmented Lyapunov Krasovskii functional (LKF) utilizing triple integral terms and the descriptor transformation is employed to this aim. In addition, advanced techniques such as Wirtinger-based single and double-integral inequalities, delay decomposition technique combined with the reciprocally convex approach, as well as a few effective free-weighting matrices are employed to achieve less conservative stability conditions. Comprehensive benchmarking numerical examples and simulation studies demonstrate the effectiveness of the proposed stability criteria with respect to some recently published results. The efficacy of the modern integral inequalities are also emphasized against the conventional Jensen׳s inequalities.

On unknown-Input Functional Observability of linear systems

Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability is introduced, and it is used as a certificate of the convergence of our algorithm. The proposed procedure looks for a number of additional auxiliary functions to be augmented to the original functions desired for reconstruction. The resulting UIFO is proper, and minimal (of minimum possible order). Moreover, the algorithm does not need the system to be unknown-input observable. A numerical example shows the procedure as well as the effectiveness of the proposed algorithm.

Improved delay-dependent stability criteria for telerobotic systems with time-varying delays

This paper addresses the synchronization problem of telerobotic systems, in which the master and slave robots are assumed to be serial manipulators and the communication-delays are assumed to be time-varying and nonsymmetric with known lower and upper bounds. Proportional derivative, proportional, and position-force control structures are considered for passive and nonpassive human operator. Using the Lyapunov-Krasovskii methodology, delay-dependent stability conditions of the closed-loop system are established in the form of linear matrix inequalities. The stability criteria derived in this paper is shown to be less conservative than some of the existing results within the literature, and they amend the calculation of the control parameters and ensure the stability and transparency of the system for larger bounds of communication-delays. Simulation studies are performed to demonstrate the effectiveness of the proposed stability criteria in obtaining a larger stability region for the system.

Functional observer design for retarded system with interval time-varying delays

ABSTRACT Functional observers are the key solution to numerous practical estimation problems, wherein full-order observers cannot be applied. This paper studies the novel problem of minimum-order functional observer design for time-delay systems with interval time-varying state delays. Moreover, unlike the majority of the existing papers on this topic, which consider either small or unknown delay rates, the delay derivative is assumed to possess an upper bound not limited to be less than one. A new augmented Lyapunov–Krasovskii functional with triple integral terms is employed to derive less conservative delay-dependent sufficient conditions for the stability of the closed-loop observer dynamics, which are expressed in terms of linear matrix inequalities. In addition, contemporary techniques such as Wirtinger-based single- and double-integral inequalities, delay splitting scheme, reciprocally convex approach and convex combination technique, along with the descriptor transformation, are adopted in constructing the new stability criterion that is exploited for obtaining the observer parameters. A genetic-algorithm-based searching schema is proposed to optimally tune a number of weighting parameters in the observer design procedure. Numerical examples and simulation results are demonstrated to confirm the effectiveness and the superiority of the proposed observer design algorithm.

Partial state estimation of LTI systems with multiple constant time-delays

Abstract Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 – delay-dependent , and 2 – internal-delay independent . The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen׳s inequality, and improved Park׳s inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

Functional observer design with application to pre-compensated multi-variable systems

Partial state estimation of dynamical systems provides significant advantages in practical applications. Likewise, pre-compensator design for multi variable systems invokes considerable increase in the order of the original system. Hence, applying functional observer to pre-compensated systems can result in lower computational costs and more practicability in some applications such as fault diagnosis and output feedback control of these systems. In this note, functional observer design is investigated for pre-compensated systems. A lower order pre-compensator is designed based on a H2 norm optimization that is designed as the solution of a set of linear matrix inequalities (LMIs). Next, a minimum order functional observer is designed for the pre-compensated system. An LTI model of an irreversible chemical reactor is used to demonstrate our design algorithm, and to highlight the benefits of the proposed schemes.

Minimal multi-functional observers for linear systems using a direct approach

The direct approach in designing functional observers was first presented in [1] for estimating a single function of the states of a Linear Time-Invariant (LTI) system. One of the benefits of the direct scheme is that it does not require solving the interconnected Sylvester equations that appear in the other observer design approaches. In the present paper, the direct approach is extended to reconstruct multiple functions of the states in such a way that the minimum possible order of the observer is achieved. The observer is designed so that an asymptotic functional observer can be obtained with arbitrary convergence rate. In the proposed methodology, it is not necessary that a reduced order observer exists for the desired functions to be estimated. To release this limitation, an algorithm is employed to find some auxiliary functions in the minimum required number to be appended to the desired functions. This method assumes that the system is functional observable. This assumption however is less restrictive than the observability and detectability conditions of the system. A numerical example and simulation results explain the efficacy and the benefits of the proposed algorithm.

A delay-dependent functional observer for linear time-invariant systems with input delay

A delay-dependent functional observer is designed for linear time-invariant (LTI) systems with time-varying input delay. Compared to delay-free observers, delay-dependent functional observers are less conservative and cover more systems. The designed functional observer is with minimum possible order (minimal). Necessary and sufficient conditions of the existence of the observer and asymptomatic stability of it are illustrated. The proposed observer is extended to multiple input delayed systems with time-varying delays. An algorithm is developed for designing of the minimal order observer based on the methodology of this paper. Two numerical examples and simulations are used to support our proposed methodology.