Related Experiment Video
Updated: May 20, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
Published on: August 15, 2020
Robust H∞ control of uncertain switched systems defined on polyhedral sets with Filippov solutions
Mohamadreza Ahmadi1, Hamed Mojallali, Rafael Wisniewski
1Department of Electrical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran. mrezaahmadi@ieee.org
Abstract:
This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Carathéodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov solutions. Subsequently, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H(∞) performance are presented. Furthermore, these results has been generalized to the case of piecewise affine systems. Finally, a V-K iteration algorithm is proposed to deal with the aforementioned bilinear matrix inequalities. The validity of the proposed method is verified through the analysis of two simulation examples.
Related Concept Videos
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
State Space Representation
Consider an RLC circuit, a...
Routh-Hurwitz Criterion I
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Time-Domain Interpretation of PD Control
Consider the example of control of motor torque. Initially, a positive...
SFG Algebra
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...