Adaptive Robust Control for A Class of Nonlinear Systems with Unknown Uncertainties

The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.

Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems

In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.

Stabilization of nonlinear systems based on robust control Lyapunov function

This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization （robust practical stabilization） is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunnv function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.

LYAPUNOV-TYPE STABILIZATION FOR NONLINEAR UNCERTAIN SYSTEMS AND NONLINEAR H~∞ CONTROL

The local robust stabilization for a class of nonlinear uncertain systems is studied. The robustness concept of Lyapunov type stabilizability for nonlinear uncertain systems is defined. Under the norm bounded structured condition, two cases for uncertainty in control matrix are taken to discuss Lyapunov type stabilizability of systems. The sufficient conditions of Lyapunov type stabilization are given from differential geometry and nonlinear H ∞ control of view, respectively.

Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty

This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.

Robust stabilization of general nonlinear systems with structural uncertainty

This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.

Robust Output Practical Stability of Time-Varying Nonlinear Control Systems via Indefinite Lyapunov Functions

This paper focuses on studying the problem of robust output practical stability of timevarying nonlinear control systems. The main innovation lies in the fact that the proposed approach for stability analysis allows for the computation of bounds that characterize the asymptotic convergence of solutions to a small ball centered at the origin using a Lyapunov method with a definite derivative.Under different conditions on the perturbation, the authors demonstrate that the system can be globally robustly asymptotically output stable by designing a candidate feedback controller. Finally, three examples are given to illustrate the practical implications and significance of the theoretical results.

The Robust Stabilizing Feedback for a Class of Nonlinear Uncertain Neutral Systems with Multiple Time Delays

The stabilization of a class of neutral systems with multiple time-delays is considered. To stabilize the neutral system with nonlinear uncertainty, a state feedback control law via compound memory and memoryless feedback is derived, by constructed Lyapunov functional, delay-independent stability criteria are proposed that are sufficient to ensure a uniform asymptotic stability property. Finally, two concise examples are provided to illustrate the feasibility of our results.

Further Result on Robust Stabilization for Uncertain Nonlinear Time-delay Systems

为一般不明确的非线性的时间延期系统的柔韧的稳定控制器的系统的递归的设计方法在这份报纸被调查。一条延期无关的州的反馈控制法律能被递归地构造 Lyapunov-Razumikhin 功能获得。以便柔韧的稳定控制法律的设计没有为系统的任何限制，由一些设计技术，对 Razumikhin 条件的应用程序内在的障碍才能被移开。

ROBUST STABILIZATION FOR MULTI-INPUT POLYTOPIC NONLINEAR SYSTEMS

This paper deals with the problem of the stabilization for multi-input polytopic nonlinear systems. Based on the robust control Lyapunov function, a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controller is derived. It is shown that the obtained sufficient condition is also necessary if there exists a state feedback controller such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. Moreover, a universal formula for constructing stabilizing controller is proposed and the existence of the corresponding Lyapunov function is proven. Particularly, a Lyapunov function is constructed for the polytopic nonlinear system in canonical form. Finally, the feasibility of the proposed control law is verified by a numerical example.

Stability Criteria for Large－Scale Linear Systems with Structured Uncertainties

The robust stability analysis for large scale linear systems with structured time varying uncertainties is investigated in this paper.By using the scalar Lyapunov functions and the properties of M matrix and nonnegative matrix,stability robustness measures are proposed.The robust stability criteria obtained are applied to derive an algebric criterion which is expressed directly in terms of plant parameters and is shown to be less conservative than the existing ones.A numerical example is given to demonstrate the stability criteria obtained and to compare them with the previous ones.

Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method

This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonian function method. Firstly, based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback, two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation, and a sufficient condition for two closed-loop systems to be impulse-free is given. The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique, based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems. Secondly, the case of more than two nonlinear descriptor systems is investigated, and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization, respectively. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.

Two fuzzy internal model control methods for nonlinear uncertain systems

Purpose-The purpose of this paper is to use the internal model control to deal with nonlinear stable systems affected by parametric uncertainties.Design/methodology/approach-The dynamics of a considered system are approximated by a Takagi-Sugeno fuzzy model.The parameters of the fuzzy rules premises are determined manually.However,the parameters of the fuzzy rules conclusions are updated using the descent gradient method under inequality constraints in order to ensure the stability of each local model.In fact,without making these constraints the training algorithm can procure one or several unstable local models even if the desired accuracy in the training step is achieved.The considered robust control approach is the internal model.It is synthesized based on the Takagi-Sugeno fuzzy model.Two control strategies are considered.The first one is based on the parallel distribution compensation principle.It consists in associating an internal model control for each local model.However,for the second strategy,the control law is computed based on the global Takagi-Sugeno fuzzy model.Findings-According to the simulation results,the stability of all local models is obtained and the proposed fuzzy internal model control approaches ensure robustness against parametric uncertainties.Originality/value-This paper introduces a method for the identification of fuzzy model parameters ensuring the stability of all local models.Using the resulting fuzzy model,two fuzzy internal model control designs are presented.

Design of controllers for a class of switched nonlinear systems based on backstepping method

The backstepping method is applied to a certain class of switched nonlinear systems to design state feedback controllers and a switching law based on multi-Lyapunov functions.The state feedback controllers and the switching law that can stabilize the system are developed.The switched nonlinear systems with uncertainties can be stabi-lized robustly by using the proposed method.Finally,simu-lation results show the effectiveness of the method.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

Global robust output regulation of lower triangular systems with nonlinear exosystems and its application

This paper studies the global robust output regulation problem for lower triangular systems subject to nonlinear exosystems. By employing the internal model approach, this problem can be boiled down to a global robust stabilization problem of a time-varying nonlinear system in the cascade-connected form. Then, a set of sufficient conditions for the solvability of the problem is derived, and thus, leading to the solution to the global robust output regulation problem. An application of the main result of this paper is also proposed.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

Integralinput-to-statestability ystemswithsmalldelays Integral input-to-state stability of systems with small delays

We consider how small delays affect the integral-input-to-state stability(iss)property for a system.Our result is similar to the input-to-state stability(Iss)result obtained in[1]:the iss property will be preserved in a practical and semi-global manner if the delay interval is small enough.However,since the iss quantifies the robust stability in terms of a generalized Li norm of the inputs instead of a generalized Loo norm of the inputs for the Iss case,the techniques and proofs for the Iss case do not apply to the iss case directly.While the proofs in[1]are based on the Lyapunov-Razumikhin approach,our proofs are based on the iss-Lyapunov functions for the zero-delay system.In addition to the interest by its own in showing how the iss property is affected by small delays,the result also serves to the study of the iss property for singularly perturbed systems.

A NOTE ON NONLINEAR ROBUST H_∞ ALMOST DISTURBANCE DECOUPLING PROBLEM WITH STABILITY

For a class of SISO nonlinear control systems with parameter uncertainty an almost disturbance decoupling problem with stability is defined and investigated. Back stepping technique provides a practical design method of controller, under which the $L2$ gain from the disturbance to the controlled output can be arbitrarily small subject to nonlinear uncertainties and the close-loop system is internally asymptotically stable.