We consider a novel method to design H-infinity observers for a class of uncertain nonlinear systems subject to unknown inputs. First, the main system dynamics are rewritten as an augmented system with state vector including both the state vector of the main system and the unknown inputs. Then, we design a H-infinity reduced-order observer to estimate both state variables and unknown inputs simultaneously. Based on a Lyapunov functional, we derive a sufficient condition for existence of the designed observer which requires solving a nonlinear matrix inequality. To facilitate the observer design, the achieved condition is formulated in terms of a set of linear matrix inequalities (LMI). By extending the proposed method to a multiobjective optimization problem, the maximum bound of the uncertainty and the minimum value of the disturbance attenuation level are found. Finally, the proposed observer is illustrated with an example.

We present a robust H∞ observer for a class of nonlinear discrete-time systems. The class under study includes an unknown time-varying delay limited by upper and lower bounds, as well as time-varying para- metric uncertainties. We design a nonlinear H∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time-varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi-objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples.

This paper deals with the problem of observer-based controller design for a class of nonlinear systems subject to unknown inputs. A novel method is presented to design a controller using estimated state variables which guarantees all the state variables of the closed-loop system converge to the vicinity of the origin and stay there forever. This is done via satisfying several sufficient conditions in terms of nonlinear matrix inequalities. In light of linear algebra, particularly matrix decompositions, the achieved conditions will be converted to a Linear Matrix Inequality (LMI) problem to facilitate the procedure of computing the observer and controller gains. Finally, the effectiveness of the proposed method is illustrated by implementing on a highly nonlinear chaotic system.

Observer design for nonlinear systems is a well-known problem in control theory that has been studied from different perspectives. Because the system state variables are generally not always available, state estimation is an essential task in many control applications, which is why this problem has attracted considerable attention from researchers and is the main focus of this thesis.Knowing that no mathematical system can exactly model a physical system, as a control engineer we must be aware of how modeling errors might adversely affect the performance of a control system. From the observer perspective, time-delays, uncertainties and unknown inputs are familiar factors that deteriorate the observer performance on the way of design, analysis and synthesis of any type of observer. Every general observer design should be able to treat all (or at least some) of these issues explicitly and provide quantitative and qualitative results about their impact on the observer performance: consequently, the concepts of robustness, robust performance and robust design have recently become common phrases in the literature and constitute an integral part of research on observer design.Compared to the typical linear systems, observer design for nonlinear systems subject to all the aformentioned deteriorative properties presents a greater challenge for control engineers and researchers. In this thesis, the problem of observer design for a class of nonlinear systems, both discrete and continuous-time, subject to time delay, structured uncertainty and unknown inputs, is investigated. The study shows that by using the upper and lower bounds of the time delay, this parameter can be excluded in the observer structure under some constraints. Moreover, a novel method for designing an Unknown Input Observer (UIO) for a class of nonlinear systems is proposed, which makes the observer capable to satisfy desired performance even inthe presence of unknown inputs. Based on the UIO structure, one step further is taken, and a multiobjective optimization approach for state estimation and unknown input reconstruction is proposed that makes the designed observer not only robust against unknown inputs but also able to reconstruct them under some provided linear matrix inequality (LMI) conditions. In light of linear algebra, note that LMI serves as an important tool in this thesis, significantly facilitating the proposed observer designs.

In this article, a combined networked switching output feedback control scheme, with a (Formula presented.)-region stability performance improvement module is presented. The network induced time delays, that are considered to be time varying and integer multiples of the sampling period, are being embedded in the system model, by state augmentation. The resulting model of the overall networked closed-loop system is switching, with the current measured round-trip time delay acting as the switching rule. Based on this modelling approach, a Linear Matrix Inequality (LMI) tuned switching output feedback controller is designed. The proposed approach establishes robustness against time delays and is able to guarantee the overall stability of the switching closed-loop system. Integrated in the controlled synthesis phase, an LMI tuned performance improvement module is being introduced, based on (Formula presented.)-region stability. Multiple simulation results are being presented that prove the efficacy of the proposed scheme.

We consider a novel method to design a H∞ filter for a class of nonlinear systems subject to unknown inputs. First, we rewrite the system dynamics as a descriptor system. Then, we design a robust H∞ reduced-order filter to estimate both state variables and unknown inputs at the same time. Based on a Lyapunov functional, we derive a sufficient condition for existence of the designed filter which requires solving a nonlinear matrix inequality. The achieved condition is further formulated in terms of a linear matrix inequality (LMI) that is straightforward to solve by popular methods. Finally, the proposed filter is illustrated with an example.

We consider a novel method to design an observer for a class of nonlinear discrete-time systems with unknown inputs. Based on Lyapunov functional, we derive a sufficient condition for existence of the designed observer which requires solving a nonlinear matrix inequality. In light of linear algebra, the achieved condition will be formulated in terms of linear matrix inequality (LMI) that can be solved by popular methods easily. Compared to recent researches, the developed approach shows a significant better performance than other techniques previously published in literature and is less conservative in terms of Lipschitz constant. Finally, the proposed observer is illustrated by implementing the proposed method on a single- link flexible manipulator and the results are compared to some recent similar researches in terms of performance and conservativeness.

In this paper, we address global non-fragile control and synchronization of a new fractional order chaotic system. First we inspect the chaotic behavior of the fractional order system under study and also find the lowest order (2.49) for the introduced dynamics to remain chaotic. Then, a necessary and sufficient condition which can be easily extended to other fractional-order systems is proposed in terms of Linear Matrix Inequality (LMI) to check whether the candidate state feedback controller with parameter uncertainty can guarantee zero convergence of error or not. In addition, the proposed method provides a global zero attraction of error that guarantees stability around all existing equilibrium points. Finally, numerical simulation are employed to verify the validity of the proposed algorithm.