Showing papers by "Ian R. Petersen published in 1993"

Systems with structured uncertainty: relations between quadratic and robust stability

Abstract: The relation between the notions of robust stability and quadratic stability for uncertain systems with structured uncertainty due to both real and complex parameter variations is discussed. Examples are presented to demonstrate that for systems containing at least two uncertain blocks, the notions of robust stability for complex parameter variations and quadratic stability for real parameter variations are not equivalent. A byproduct of these examples is that, for this class of systems, quadratic stability for real perturbations need not imply quadratic stability for complex perturbations. This is in stark contrast with the situation in the case of unstructured uncertainty, for which it is known that quadratic stability for either real or complex perturbations is equivalent to robust stability for complex perturbations, and thus equivalent to a small gain condition on the transfer matrix that the perturbation experiences. >

Guaranteed cost LQG control of uncertain linear systems

Abstract: This paper presents a Riccati equation approach to the output feedback quadratic stabilization of uncertain systems. The uncertain systems under consideration depend on a norm-bounded time-varying matrix of uncertain parameters. A feature of the approach taken is that it involves the minimisation of a certain bound on an LQG cost function. The results were obtained by combining results on an optimal guaranteed cost linear quadratic regulator problem for uncertain systems and an optimal guaranteed cost state estimation problem for uncertain systems. >

Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty

Abstract: This paper considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty. The uncertainties in the system are described by a certain integral quadratic constraint which allows for a rich class of uncertainties including nonlinear dynamic time-varying uncertainty. The notion of stabilizability considered is that of absolute stabilizability. The main results show that the question of absolute stabilizability for the class of uncertain linear systems under consideration is equivalent to the existence of a solution to a corresponding "diagonally scaled" H/sup /spl infin// control problem. A consequence of this result is the fact that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control. >

H infinity control of flexible slewing link with active damping

Abstract: This paper presents some initial results based on H(infinity ) controller designs for a flexible slewing piezoelectric laminate beam. A two-input-one-output model of a piezoelectric laminate is used; slewing torque and piezoactuator voltage are the two inputs and the tip-position is the output. Two control design examples are used to demonstrate the utility of active control in damping the vibrations in a slewing motion.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.