A Frequency Condition for the Generalized Recurrent Difference in the Synthesis of H∞-Suboptimal, Decentralized, and Robust Regulators

Abstract

A new approach to designing control laws under uncertainty produces easily verifiable tests for their generalized recurrent differences and does not require the solution of matrix equations or inequalities. This test is expressed as a frequency inequality, which is verified by verifying whether a polynomial has a real positive root of odd multiplicity. The underlying principles of the method are the necessary and sufficient conditions for a given stabilizing linear feedback to be the local minimax control satisfying the Bellman–Isaac inequality in a differential game with a general quadratic functional. The design of controls for Lur'e systems and systems with uncertain bounded parameters as well as the design of i>H∞-suboptimal regulators and decentralized controls for multiconnected systems with unknown cross-coupling are shown to involve a local minimax control problem.