Abstract The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.
The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix inequalities for the Dstable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-lime linear systems with polytopic uncertainties.
Abstract Stability analysis and design for continuous-time proportional plus derivative state observers is presented in the paper with the goal to establish the system state and actuator fault estimation. Design problem accounts a descriptor principle formulation for non-descriptor systems, guaranteing asymptotic convergence both the state observer error as fault estimate error. Presented in the sense of the second Lyapunov method, an associated structure of linear matrix inequalities is outlined to possess parameter existence of the proposed estimator structure. The obtained design conditions are verified by simulation using a numerical illustrative example.
Abstract The paper provides the minimal necessary modifications of linear matrix inequality conditions for the mixed H2/H∞ control design as well as for the augmented observer-based fault estimation to be mutually compatible in joint design of integrated fault estimation and fault tolerant control. To be possible, within this integration, to design the controller which guarantees a pre-specified H∞ norm disturbance attenuation level, the design conditions has to be regularized using the H2 performance index and, moreover, augmented fault observer must be of enforced dynamics. Analyzing the ambit of performances given on the mixed H2/H∞ design, the joint design conditions are formulated as a minimization problem subject to convex constraints expressed by a system of LMIs. The feasibility of the conditions is demonstrated by a numerical example.
Abstract The H∞ norm approach to virtual actuators design, intended to Takagi-Sugeno fuzzy continuous-time systems, is presented in the paper. Using the second Ljapunov method, the design conditions are formulated in terms of linear matrix inequalities in adapted bounded real lemma structures. Related to the static output controller, and for systems under influence of single actuator faults, the design steps are revealed for a three-tank system plant.