Robust Stabilization by Linear Output Delay Feedback

This paper addresses the problem of global output feedback stabilization for a class of upper-triangular systems with delay in the input. By using a linear observer, a linear dynamic output feedback control law is explicitly constructed to globally stabilize the system. To dominate the nonlinear perturbing terms and handle the case with a larger input delay, a tunable scaling gain is introduced to the controller by using a coordinates change. With the help of appropriate Lyapunov-Krasoveskii functional and feedback domination approach, it is shown that upper-triangular nonlinear system with arbitrary large input delay can be globally stabilized by the proposed output feedback controller with appropriate gains.

Full probabilistic solution of a finite dimensional linear control system with random initial and final conditions

The problem of robust stabilisation is considered for uncertain systems using linear static output feedback (SOF) controllers and linear dynamical output feedback (DOF) controllers with fixed order. The existence conditions of output feedback controllers are given by matrix inequalities and result in some nonlinear optimisation problems. A class of uncertain plants whose nominal systems are minimal phase with a full row rank can be robustly stabilised by an SOF controller and DOF controller with any order, and controllers can be obtained by solving some linear matrix inequalities (LMIs). The method is demonstrated by two numerical examples

Global output-feedback stabilization for high-order nonlinear systems with unknown control coefficients

Robust passivity and feedback design for minimum-phase nonlinear systems with structureal uncertainty

Global stabilization of a class of partially known nonnegative systems

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptotics with respect to input noises and can be used for numerical differentiation as well. The resulting controllers provide for the full output-feedback real-time control of any output variable of an uncertain dynamic system, if its relative degree is known and constant. The theoretical results are confirmed by computer simulation.

This paper concerns the problems of robust stability analysis and stabilization for uncertain linear system with time-varying delay. In order to obtain a robust stability criterion with less conservative for uncertain linear delay system, a quadratic integral inequality is improved by matrix decomposition. Further, two different kinds of controller, i.e., linear memoryless state feedback controller and linear state feedback controller with state delay, are derived in terms of the robust stability criteria. Two numeral examples are provided to demonstrate the validity of the proposed methods.

In this paper a necessary and sufficient condition for a nonlinear system of the form /spl Sigma/, given by x(k+1)=f(x(k))+g(x(k))u(k), y(k)=h(x(k))+J(x(k))u(k), to be lossless is given, and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero-state observable. Then, we investigate conditions under which /spl Sigma/ can be rendered lossless via smooth state feedback. In particular, we show that this is possible if and only if the system in question has relative degree /spl lcub/0,...,0/spl rcub/ and has lossless zero dynamics. Under suitable controllability-like rank conditions, we prove that nonlinear systems having relative degree /spl lcub/0,...,0/spl rcub/ and lossless zero dynamics can be globally stabilized by smooth state feedback. As a consequence, we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable. The global stabilization problem of the nonlinear system /spl Sigma/ without output is also investigated in this paper by means of feedback equivalence. Some of the results are parallel to analogous ones in continuous-time, but in many respects the theory is substantially different and many new phenomena appear.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this article, we investigate the problem of simultaneously steering an uncountable family of finite-dimensional time-varying linear systems with the same control signal. This class of control problems motivates further research in the new subject of control theory called Ensemble Control, a notion coming from the study of complex spin dynamics in nuclear magnetic resonance spectroscopy and imaging. We derive the necessary and sufficient controllability conditions and an accompanying analytical optimal control law for an ensemble of finite-dimensional time-varying linear systems. We show that ensemble controllability is in connection with singular values of the operator characterizing the system dynamics. In addition, the problem of optimal ensemble control of harmonic oscillators is studied to demonstrate the controllability results. We show that the optimal solutions are pertinent to the study of time-frequency limited signals and prolate spheroidal wave functions. A systematic study of ensemble control systems has immediate applications to dynamical systems with parameter uncertainty as well as to wide-ranging areas such as neuroscience and quantum control. The work in ensemble control will foster further developments in mathematical control and systems theory.

Algebraic system theory: an analyst's point of view

In this paper we attempt to describe a circle of ideas which makes possible a unified exposition of a large part of linear algezbra, operator theory and both finite and infinite dimensional multivariable linear systems. As the title suggests the unifying conzcepts will be those of functional models, module theory and various factorizations of polynomial and analytic matrix valued functions. The full exposition of the ideas presented here will be the theme of a forthcoming monograph [20].

From time series to linear system—Part I. Finite dimensional linear time invariant systems

Previously, we posted the following question concerning the array realization problem: Assume that one or more (mathematical) model realizes (faithfully describes) an arbitrary (two dimensional) array; if two such models exist that realize the array, then are these models isomorphic? The solution to this question is the array realization theorem: Canonical commutative linear representative systems necessarily exist that realize an arbitrary array, and these systems are identical excluding isomorphism. An investigation of finite dimensional canonical commutative linear representation systems that can be dealt with on a computer is performed. An algorithm is provided that realizes any given finite dimensional array. In this paper, an efficient coding (communications channel coding) is described for arrays that result from the structure problem of commutative linear representative systems based on these results and its solution. This structure problem is an extension of the structure problem occurring in linear system theory to a structure theorem for commutative linear representative systems. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(3): 58–68, 1999

Consistent estimation of real NMP zeros in stable LTI systems of arbitrary complexity