Finding maximum linear subsystems of nonlinear systems with outputs

The focus of this paper is to find the maximum input-output linearized subsystem. Necessary and sufficient conditions are presented under which there exist a static state feedback and a coordinate change to input-output linearize the system so that the linear subsystem has the largest dimension. A systematic method is also developed to compute the desired feedback and coordinate change     

Robust control for a class of state-constrained high-order switched nonlinear systems with unstable subsystems

This paper addresses the issue of robust stabilisation for a class of state-constrained high-order switched nonlinear systems whose subsystems are allowed to be all unstabilizable. A novel robust control scheme is established based on effective coupling of the technique of adding a power integrator and the method of multiple barrier Lyapunov functions. Explicitly, a sufficient condition for robustly stabilising the resulting closed-loop system in a domain is presented, which meanwhile can also guarantee that the violation of the constraints does not happen. Moreover, in the switching law design, we do not require the connection of barrier Lyapunov functions for two adjacent subsystems, and even a certain amount of jump is also allowed. Finally, the effectiveness of the provided control strategy is demonstrated via a simulation example.     

Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems

Exponential stability and robust exponential stability relating to switched systems consisting of stable and unstable nonlinear subsystems are considered in this study. At each switching time instant, the impulsive increments which are nonlinear functions of the states are extended from switched linear systems to switched nonlinear systems. Using the average dwell time method and piecewise Lyapunov function approach, when the total active time of unstable subsystems compared to the total active time of stable subsystems is less than a certain proportion, the exponential stability of the switched system is guaranteed. The switching law is designed which includes the average dwell time of the switched system. Switched systems with uncertainties are also studied. Sufficient conditions of the exponential stability and robust exponential stability are provided for switched nonlinear systems. Finally, simulations show the effectiveness of the result.     

BIBO stability of fractional-order controlled nonlinear systems

The BIBO stability of fractional-order controlled nonlinear systems is investigated in this paper. By introducing the properties of some Mittag-Leffler functions and using an inequality satisfied by the Caputo derivative of a Lyapunov function, sufficient conditions to guarantee the BIBO stability are firstly presented. Then, the boundedness of solutions of the fractional financial system and the fractional low-order atmospheric circulation system are proved by the established stability results. Besides, two illustrative examples verify the theoretical results.     

Adaptive fuzzy decentralized control for interconnected MIMO nonlinear subsystems

This paper describes an adaptive fuzzy control strategy for decentralized control for a class of interconnected nonlinear systems with MIMO subsystems. An adaptive robust tracking control schemes based on fuzzy basis function approach is developed such that all the states and signals are bounded. In addition, each subsystem is able to adaptively compensate for disturbances and interconnections with unknown bounds. The resultant adaptive fuzzy decentralized control with multi-controller architecture guarantees stability and convergence of the output errors to zero asymptotically by local output-feedback. An extensive application example of a three-machine power system is discussed in detail to verify the effectiveness of the proposed algorithm.     

Stability and asynchronous stabilization for a class of discrete-time switched nonlinear systems with stable and unstable subsystems

The stability analysis and asynchronous stabilization problems for a class of discrete-time switched nonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzy model is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems are modeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions (FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for the open-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions for the closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results and asynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numerical examples are provided to illustrate the effectiveness of the results obtained.     

A small gain theorem for systems with non-causal subsystems

Small gain theorems are used to verify the stability of a feedback interconnection of causal stable systems. In this work, we extend the small gain condition to test the stability of a feedback interconnection of two stable systems at least one of which is non-causal. This result may find application in the robust controller design for time-delay systems.     

Identifying subsystems in information systems analysis

The paper discusses five main criteria for the construction of subsystems of an information system. The criteria are flexibility/changeability, separability, comprehensibility, integrability and data usage and/or creation. Two procedures based on the data usage and/or creation criterion are described. These procedures are used to determine the composition of each subsystem, keeping the other four criteria in focus. An application of the methodology to a sample data is presented.     

On symmetric and unity interconnections between three nonlinear subsystems

A specific type of interconnection is examined with regard to three nonlinear subsystems in this communique. Further, the two possibilities of this specific linear interconnection are investigated in detail. For each kind of interconnection, conditions for the global stability of the overall system are derived, via the Popov method, which are simple and easy to apply. The conditions are rather conservative in nature, though a certain amount of flexibility does exist in the choice of the various parameters in the event of constraints other than stability are to be satisfied. An example is included to illustrate the utility of the conditions.     

Numerical investigation of attainability sets of nonlinear controlled differential systems

The paper is devoted to schemes of approximation of attainability sets of nonlinear controlled differential systems where the problem of program control optimization is an “elementary operation.” The results of numerical experiments are represented.     

External estimates of the reachability sets of nonlinear controlled systems

Consideration was given to formation of the external estimates of the reachability sets of the nonlinear controlled systems in the form of the level sets of the functions satisfying the differential Hamilton-Jacobi inequalities. The trajectories of the nonlinear system are estimated by modifying the estimates of its linear part. The constructions proposed are based on comparing the systems of differential inequalities. Applications of the reachability sets of the multivariable controlled systems with nonlinear cross connections to the ellipsoidal estimates were examined.     

Structure analysis of periodically controlled nonlinear systems via the stroboscopic approach

It is shown that an efficient structure analysis of periodically controlled nonlinear systems is possible by use of the computer simulation technique coupled with the stroboscopic approach. The existence and stability of every periodic state can be determined together with the dynamic behavior in the neighborhood of these periodic states. Especially, the proposed technique seems to be the only way for finding out periodic states of the saddle mode.     

Stability analysis of interconnected systems with possibly unstable subsystems

A direct method is presented for stability analysis of nonlinear interconnected dynamical systems. A new scalar Lyapunov function is considered as weighted sum of individual Lyapunov functions for each free subsystem and individual scalar functions related separately to each connection. Sufficient conditions are obtained for asymptotic stability of the equilibrium state by testing the definity of two constant square matrices whose dimension is equal to the number of subsystems. This method can assure stability of systems with possible unstable subsystems. A simple numerical example is included to illustrate this theory.     

Input-output pseudolinearization for nonlinear systems

An input-output pseudolinearized system has the property that its family of linearizations about constant operating points has input-output behavior that is independent of the operating point. We develop a necessary and sufficient condition for existence of a state feedback and state coordinate change that transforms a given system into a pseudo-normal form that is input-output pseudolinearized. These ideas are applied to obtain new approaches to approximate tracking and approximate inversion of nonlinear systems     

Observers for discrete-time nonlinear systems

The problem of observers for discrete-time nonlinear systems has been considered and a simple, easy-to-implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems. Some numerical examples show the effectiveness of the proposed observer.     

Controlled invariance for nonlinear systems

Necessary and sufficient conditions are derived for "(A, B)- invariance," called here controlled invariance, for nonlinear systemsdot{x} = f(x, u). The obtained results generalize and elucidate already known results about systemsdot{x} = A(x) - sum min{i=1}max{m} =u_{i}B_{i}(x). A new and direct differential geometric interpretation of the concept of controlled invariance and the derived conditions is given.