Dynamic controller synthesis guaranteeing L/sub 2/-gain for time-controlled switched systems

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

“…Thus, by the definitions of the subregions, we have set up a selection law that leads to switching control with hysteresis. Switching with hysteresis avoids chattering phenomena and, in analysis and synthesis based on Lyapunov or storage functions, allows us to utilize a class of discontinuous functions as a candidate of a Lyapunov and/or storage function [6,7,9,10]. Define  = {1, 2, … , N} and…”

“…The following parameter-dependent LMI condition is a generalization of L 2 -gain analysis for time-controlled switched systems with an lower bound of dwell-time [6], which is an adaptation of the method of multiple quadratic Lyapunov or storage functions [19] to the switched system (7)-(8) whose continuous dynamics is given by LPV systems, with also applying the standard technique of scaled H ∞ control [21]. Lemma 2 ([6]).…”

“…As a generalization of [6], we can linearize the matrix inequalities (10), (11) and (15) as in the following Theorem.…”

“…In this paper, we consider gain‐scheduled controllers that switch the coefficient matrices of an LTI controller and reset the state of the controller according to hysteresis of the scheduling parameter. Based on the stability and L 2 ‐gain analysis and synthesis methods for switched systems developed in Masubuchi and Tsutsui , we show an LMI‐based synthesis method of the coefficient matrices of a switched LTI controller with a reset law of the controller state. Unlike the previous result of , the state reset law as well as the switched LTI control law depends only on the measured output.…”

“…The rest of the paper is organized as follows. In Section 2, we formulate a switching control law by following with hysteresis switching and show LMIs for synthesis based on Masubuchi and Tsutsui . Also, we consider tuning of the controller state reset law to reduce jump of control input.…”