Integral Quadratic Constraint Framework Research Articles

Robustness Analysis of a Nonlinear Missile Autopilot via Integral Quadratic Constraints

In this paper, integral quadratic constraints (IQC) and linear parameter varying modelisation are used to analyse the stability robustness of an uncertain non linear control system. A pitch-axis model of a highly manoeuvrable missile is presented and a nonlinear control based on dynamic inversion is applied. Stability is then analysed in presence of uncertainties on the aerodynamic coefficients via the IQC framework.

Lyapunov functionals in complex μ analysis

Conditions for robust stability of linear time-invariant systems subject to structured linear time-invariant uncertainties can be derived in the complex /spl mu/ framework, or, equivalently, in the framework of integral quadratic constraints. These conditions can be checked numerically with linear matrix inequality (LMI)-based convex optimization using the Kalman-Yakubovich-Popov lemma. We show how LMI tests also yield a convex parametrization of (a subset of) Lyapunov functionals that prove robust stability of such uncertain systems. We show that for uncertainties that are pure delays, the Lyapunov functionals reduce to the standard Lyapunov-Krasovksii functionals that are encountered in the stability analysis of delay systems. We demonstrate the practical utility of the Lyapunov functional parametrization by deriving bounds for a number of measures of robust performance (beyond the usual H/sub /spl infin// performance); these bounds can be efficiently computed using convex optimization over linear matrix inequalities.

New IQC for quasi‐concave nonlinearities

AbstractA new set of integral quadratic constraints (IQC) is derived for a class of ‘rate limiters’, modelled as a series connections of saturation‐like memoryless nonlinearities followed by integrators. The result, when used within the standard IQC framework (in particular, with finite gain/passivity‐based argiments, Lyapunov theory, structured singular values, etc.), is expected to be widely useful in nonlinear system analysis. For example, it enables ‘discrimination’ between ‘saturation‐like’ and ‘deadzone‐like’ nonlinearities and can be used to prove stability of systems with saturation in cases when replacing the saturation block by another memoryless nonlinearity with equivalent slope restrictions makes the whole system unstable. In particular, it is shown that the L2 gain of a unity feedback system with a rate limiter in the forward loop cannot exceed \sqrt{2}.In addition, a new, more flexible version of the general IQC analysis framework is presented, which relaxes the homotopy and boundedness conditions, and is more aligned with the language of the emerging IQC software. Copyright © 2001 John Wiley & Sons, Ltd.

Efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems

Sufficient conditions for the robust stability of a class of uncertain systems, with several different assumptions on the structure and nature of the uncertainties, can be derived in a unified manner in the framework of integral quadratic constraints. These sufficient conditions, in turn, can be used to derive lower bounds on the robust stability margin for such systems. The lower bound is typically computed with a bisection scheme, with each iteration requiring the solution of a linear matrix inequality feasibility problem. We show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue minimization problem, which can be solved very efficiently using standard algorithms. We illustrate this with several important, commonly encountered special cases: diagonal, nonlinear uncertainties; diagonal, memoryless, time-invariant sector-bounded (Popov) uncertainties; structured dynamic uncertainties; and structured parametric uncertainties. We also present a numerical example that demonstrates the computational savings that can be obtained with our approach.

Analysis of Rate Limiters Using Integral Quadratic Constraints

It is shown It is shown how the framework of integral quadratic constraints can be used to analyse systems with rate limiters, in spite of the fact that such systems can not be globally exponentially stable.The analysis is based on computation of the L2 -gain in a feedback loop involving a saturation followed by an integrator.