An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable

Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.linear-quadratic games;linear feedback Nash equilibrium;affine systems;solvability conditions;Riccati equations

Control Strategies for Complex Systems for Use in Aerospace Avionics

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryAir Force Office of Scientific Research (AFSC) / AF-AFOSR 78-363

Singular Perturbations and Time-Scale Methods in Control Theory: Survey 1976-1982

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424U.S. Air Force / AFOSR 78-363

Robust stability of differential-algebraic equations

This paper presents a survey of recent results on the robust stability analysis and the distance to instability for linear time-invariant and time-varying differential-algebraic equations (DAEs). Different stability concepts such as exponential and asymptotic stability are studied and their robustness is analyzed under general as well as restricted sets of real or complex perturbations. Formulas for the distances are presented whenever these are available and the continuity of the distances in terms of the data is discussed. Some open problems and challenges are indicated

Integral Sliding Mode Control of Lur’e Singularly Perturbed Systems

This paper investigates the integral sliding mode control problem for Lur’e singularly perturbed systems with sector-constrained nonlinearities. First, we design a proper sliding manifold such that the motion of closed-loop systems with a state feedback controller along the manifold is absolutely stable. To achieve this, we give a matrix inequality-based absolute stability criterion; thus the above problem can be converted into a matrix inequality feasibility problem. In addition, the gain matrix can also be derived by solving the matrix inequality. Then, a discontinuous control law is synthesized to force the system state to reach the sliding manifold and stay there for all subsequent time. Finally, some numerical examples are given to illustrate the effectiveness of the proposed results