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We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the topological entropy of the channel dynamics. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel.

We consider the problem of global external stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. The objective is to control such plants by a possibly nonlinear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector for all time in the presence of disturbances and Gaussian distributed initial conditions. Results for continuous-time open-loop critically stable plants as well as for a chain of integrators have been obtained before. The goal of this technical note is to extend this result to critically unstable plants. We view our contribution in this technical note as a critical step in solving the LQG control problem for linear systems subject to saturated inputs which is a research problem with a long history in our field.

We present two results on attitude estimation using vector and rate gyro measurements. The first result concerns an observer previously presented by Hamel, Mahony, and Pflimlin, with proven stability results when i) the reference vectors are stationary; or ii) the gyro measurements are unbiased. We prove semiglobal stability without either of these assumptions when a parameter projection is added, and convergence from all initial attitudes when using a resetting strategy. The second result is an algorithm for estimation of bias in the body-fixed vector measurements, which is analyzed in combination with the attitude and gyro bias observer.

We consider linear time-invariant multiple-input multiple-output systems that are controllable and observable, where each output component is saturated. We demonstrate by constructive design that such systems can be globally asymptotically stabilized by output feedback without further restrictions. This result is an extension of a previous result by Kreisselmeier for single-input single-output systems. The control strategy consists of driving the components of the output vector out of saturation one by one, to identify the state of the system. Deadbeat control is then applied to drive the state to the origin.

In this technical note, we fully characterize the dynamic response of a saturating static feedback-controlled single integrator driven by Gaussian white noise by solving the derived Fokker-Planck equation.

We demonstrate that some delay-differential equations of neutral type are, up to basis transformation, equivalent to retarded delay differential equations. In particular, for two classes of neutral delay differential equation models, we use state transformations to show that delayed derivatives can in some cases be expressed in terms of the model’s state. Hence, we obtain conditions when neutral delay differential equations can be transformed into retarded delay differential equations.

We revisit the classical problem of finding a positive diagonal solution P to the Lyapunov equation AT P + PA < 0 that minimizes the Lyapunov exponent (the maximum eigenvalue of AT P + PA) for A isin RnXn, with the aim of identifying structural properties of the Lyapunov matrix equation at the optimum. Using eigenvalue sensitivity notions together with optimization machinery, we are able to obtain an explicit characterization of the minimum Lyapunov exponent that provides such structural insight.

This paper deals with the design of linear systems with saturating actuators where the actuator limitations have to be incorporated a priori into control design. The authors take a semiglobal approach to solve some of the central control problems for such systems. These problems include stabilization, input-additive disturbance rejection, and robust stabilization in the presence of matched nonlinear uncertainties. The authors develop further the semiglobal design technology which was initiated in their earlier work (Lin and Saberi, 1995) and utilize it to deal with these control problems.

This paper is concerned with the discrete-time $H_\infty$ control problem with strictly proper measurement feedback. We derive necessary and sufficient conditions for the existence of strictly proper compensator which achieves a given $H_\infty$ norm bound. Note that contrary to the continuous time, in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator. Finally, we given an explicit formula for one controller which achieves this bound. Keywords: Discrete time systems, Hoo control problem, strictly proper controllers.

In this note the H/sub /spl infin// control problem with measurement feedback is investigated. It is well-known that for this problem, in general, we need controllers of the same dynamic order as the given system. However, in the case that some entries of the measurement vector are not noise-corrupted, we show that one can find dynamic compensators of a lower dynamical order. Note that this implies that the standard assumptions on the direct feedthrough matrices, as made in most papers on H/sub /spl infin// control, are not satisfied. Our result can be derived by using reduced order observer based controllers. >

Explicit expressions for two different cascade factorizations of any detectable left invertible nonminimum phase systems are given. The first one is a well known minimum phase/all-pass factorization by which all nonminimum phase zeros of a transfer function G(s) are collected into an all-pass factor V(s), and G(s) is written G/sub m(s)V/$ where G/sub m/s is considered as a minimum phase image of G(s). The second one is a new cascade factorization by which G(s) is rewritten as G/sub M/(s)U(s) where U(s) collects all 'awkward' zeros including all nonminimum phase zeros of G(s). Both G/sub m/(s) and G/sub M/(s) retain the given infinite zero structure of G(s). Further properties of G/sub m/(s), G/sub M/(s), and U(s) are discussed. These factorizations are useful in several applications including loop transfer recovery. >

The authors present a simple and noniterative procedure for the computation of the exact value of the infimum in the standard H/sub infinity /-optimal control with output feedback. The problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. The method is applicable to systems that satisfy the following conditions: (1) the transfer function from the control input to the controlled output is right-invertible and has no invariant zeros on the j omega axis, and (2) the transfer function from the disturbance to the measurement output is left-invertible and has no invariant zeros on the j omega axis. >

Given a system, which is not necessarily invertible and which has an unequal number of inputs, a method of 'squaring down', that is a method of designing pre-compensators and postcompensators such that the resulting system has an equal number of inputs and outputs and is invertible, is presented. The compensators are, in general, dynamic and have the property that the additional finite zeros induced by them are assignable to the open left-half complex plan. Furthermore, the compensators are asymptotically stable, and hence do not deteriorate the robustness and performance of an eventual feedback design. Also, the compensator design preserves the stabilizability, detectability, and minimum-phase properties and the infinite zero structure of the original system. Thus, a method of designing nonsquare systems by converting them to square invertible systems is introduced. Two applications of such a design philosophy, (1) diagonal decoupling with state feedback; and (2) almost disturbance decoupling with output feedback, are pointed out. >

For a general class of nonlinear singularly perturbed systems, a two-time-scale analysis and design procedure for stabilization and regulation is presented. It is shown that, under a set of conditions, the composite control proposed by Chow and Kokotovic [5], asymptotically stabilizes the desired equilibrium and produces a finite cost J uc , which tends to the cost of the slow regulator as the perturbation parameter e tends to zero. Thus, the well-posedness of the full regulator problem is established. Furthermore, under different stability requirements on the fast subsystem, explicit upper and lower bounds on J uc are obtained. Finally, for each result in this paper an upper bound on the perturbation parameter e is provided under which the result is valid.

This note presents a new canonical form for linear multivariable systems. This canonical form casts and partitions the system to the so-called component connection model (CCM). The application of this canonical form to the problem of decentralized stabilization and estimation is discussed.

This paper presents a high-gain feedback stabilizing control algorithm in which the high-gain parameter is adapted on line. The algorithm is developed for a class of nonlinear systems which can be viewed as the nonlinear counterpart of uniform rank multivariable linear systems. The system can be unknown except for a number of vital pieces of information. For single-input single-output linear systems such information is usually required in the traditional adaptive control literature.

Asymptotic and exponential stability of nonlinear singularly perturbed systems are investigated via Lyapunov stability techniques. A quadratic-type Lyapunov function for a singularly perturbed system is obtained as a weighted sum of quadratic-type Lyapunov functions of two lower order systems. Estimates of domain of attraction, of upper bound on perturbation parameter, and of degree of exponential stability are obtained. The method is illustrated by studying the stability of a synchronous generator connected to an infinite bus.

The use of local high-gain feedback to stabilize a class of nonlinear interconnected systems is studied. Classes of systems that can be stabilized, for any arbitrary interconnections, using only local high-gain feedback are identified.