The continuous- and discrete-time H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H∞-suboptimal controllers, including reduced-order controllers.

The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H∞ controllers and bear important connections with the controller order and the closed-loop Lyapunov functions.

Thanks to such connections, the LMI-based characterization of H∞ controllers opens new perspectives for the refinement of H∞ design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.

A linear matrix inequality approach to H∞ control

The purpose of this article is to provide a tutorial overview of information consensus in multivehicle cooperative control. Theoretical results regarding consensus-seeking under both time invariant and dynamically changing communication topologies are summarized. Several specific applications of consensus algorithms to multivehicle coordination are described

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Information consensus in multivehicle cooperative control

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Survey paper: Set invariance in control

We consider systems that can be described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. Under a set of technical assumptions about the perturbation and its relationship to the outputs, we present a modular observer design technique. The observers produced by this design technique consist of a modified high-gain observer that estimates the states of the system together with the full perturbation, and a parameter estimator. The parameter estimator is constructed by the designer to identify the unknown parameters by dynamically inverting a nonlinear equation. We illustrate the design technique by constructing an observer for a DC motor with friction modeled by the dynamic LuGre friction model.

https://www-robotics.jpl.nasa.gov/publications/Havard_Grip/Grip_CDC2009_nlparam.pdf

State and parameter estimation for linear systems with nonlinearly parameterized perturbations

On global external stochastic stabilization of linear systems with input saturation

We look at the stabilization and regulation problems for linear systems subject to both rate and saturation limits. With respect to stabilization we focus on semi-global stabilization. This allows one to use linear compensators. We concentrate on the state feedback, single-input case. However, the results can be extended to the measurement feedback and multi-input case.

Stabilization and regulation of linear systems with saturated and rate-limited actuators

The authors consider an H/sub 2/ optimization problem via state feedback. The problems dealt with are of general singular type which have a left invertible transfer matrix function from the control input to the controlled output. This class subsumes the regular H/sub 2/ optimization problems. The authors construct and parameterize all the static and dynamic H/sub 2/ optimal state feedback solutions. Moreover, all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues called the optimal fixed modes. Every H/sub 2/ optimal controller must assign among the closed-loop eigenvalues the set of optimal fixed modes. This set of optimal fixed modes includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and locations of pole-zero cancellations present in any H/sub 2/ optimal design. It is shown that both the sets of optimal fixed modes and optimal fixed decoupling zeros do not vary depending upon whether the static or the dynamic controllers are used. >

http://ieeexplore.ieee.org/iel5/1040/8509/00371700.pdf

Ali Saberi

Papers

State and parameter estimation for linear systems with nonlinearly parameterized perturbations

On global external stochastic stabilization of linear systems with input saturation

Stabilization and regulation of linear systems with saturated and rate-limited actuators

Construction and parameterization of all static and dynamic H/sub 2/-optimal state feedback solutions, optimal fixed modes and fixed decoupling zeros

On blocking zeros and strong stabilizability of linear multivariable systems