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This study is motivated from the investigation of vehicle suspension system with changeable damping and variant stiffness parameters. Such suspension system can be modeled as a dynamic polytope based on the mapping of affinely changed parameters. According to the polytopic dynamics decomposition, knowledge of linear time invariant system can be applied to each polytope vertex and the time variant system is solved by the polytope convex synthesis method. For time variant vehicle suspension system, the different model structures for control purposes are formulated. A quarter-car is taken as the example for demonstration in observer design and nonlinear control design.

This paper presents the polytopic modeling method and state variable observer design approach for semi-active suspension with changeable damping and variant stiffness elements. And such semi-active suspension system is suitable to be modeled as a dynamic polytopic system where the extreme vertices of damping and stiffness values are taken as the convex vertices of polytope. Thus, a dynamic polytopic model is the convex synthesis with all the vertex system dynamics and linear system theory can be applied to the system at each vertex. Herein, the conventional Kalman filter theory is utilized to design the observer for each vertex system, then the polytopic observer is formulated by a convex synthesis. The proposed observer design approach is testified by numerical study and vehicle test.

As an important class of nonlinear system, polytopic bilinear system is investigated. Combined with the properties of convex polytope, the nonlinear control for polytopic bilinear system is formulated by synthesizing nonlinear H∞ controller which is designed for polytopic bilinear system at vertices. For a semi-active suspension system with controllable damping and variant stiffness elements, it is easily modeled as a polytopic bilinear system model. In this case, the desired nonlinear control properties are pursued in making effective use of the changeable damping property while the variant stiffness is taken as the affine parameter of polytopic model. Therefore, polytopic bilinear system model could be reduced to a feasible problem by polytopic convex decomposition. Then the control problem of bilinear system model is to find a solution of nonlinear H∞ control.

State-space solutions of H∞ controller have been well developed. Hence to a real structure control design, the first step is to get a state space model of the structure. There are analytical and experimental dynamic modeling methods. As we know, it is hard to obtain an accurate model for a flexible and complex structure by FEM(Finite Element Method). Then the experimental modeling methods are used. In this paper, we use frequency domain modal analysis technique based on system FRF(Frequency Response Function) data and ERA(Eigensystem Realization Algorithm) time domain method based on system impulse response data to establish state-space model in order to design H∞ control law for the purpose of vibration suppression. The robust control implementation is exerted on a testbed (truck cab model device) with three degrees of freedom. The validity of experimental state-space modeling is testified and the obvious vibration control performances are achieved.