5 ICI Bucharest © Copyright 2012-2018. All rights reserved ISSN: 1220-1766 eISSN: 1841-429X 1. Introduction The state-space representation of systems is advantageous because of the manipulability of the matrices involved in state-space models. Accordingly, several methods have been developed to simulate the systems, to analyze their behaviours and to carry out the controller design in order to exhibit desired and/or imposed behaviours. In addition, as shown in [8] for optimal control, [24] for cascade control, [31] for robust control and [33] for minimum variance control, modelling the dynamics of complex systems by state-space models can guarantee high control system performance. A special advantage of the state-space representation is the possibility to give geometrical interpretations in relation with the stability analysis. This is caused by the intuitiveness, which results in several control design approaches based on geometrical illustrations. Some recent approaches to the analysis and design of nonlinear state-space control systems, referred to also as state- feedback control systems, are discussed as follows. The pole placement method is extended with optimization in [6] and [9], and applied to power systems stabilization. A reference state generator is designed by backstepping in [29] and included in an unmanned system control scheme. Nonlinear state-space models of rectifers are employed in [4] to perform the voltage control in microgrids, while the optimal control of hidden Markov models is investigated in [16]. A bank of reduced-order Luenberger observers is designed in [7] to locate a specifc fault source. The hybrid system-based combination of state-space partition and optimal control of multi-model for nonlinear systems is suggested in [35] and the state constrained control of nonlinear systems is treated in [3]. A nonlinear state observer for the estimation of different gas species concentration profles is proposed in [18] and a state-space approach to predictive control is given in [17]. Robustness features are added in [40] to state-space control, while the combination with fuzzy modelling and control is treated in [1, 5, 12, 20, 32]. The analysis of the state-of-the-art reveals the fact that the illustrations usually concern systems with two state variables. The generalization to systems with arbitrary number of state variables is rather complicated. This paper proposes an approach to the design of a general family of nonlinear state-space control systems. The approach is based on the original geometrical illustration of systems evolution in the state space, and makes use of Lyapunov’s direct method, the native behaviour and the desired system matrix. The approach proposed in this paper is important in the context of the state-of-the-art presented above because of two reasons. First, it is relatively simply applicable to systems with arbitrary number of state variables. Second, it is applicable to wide classes of systems generally expressed as input-affne nonlinear systems. They include An Approach to the Design of Nonlinear State-Space Control Systems Claudiu POZNA 1,2 , Radu-Emil PRECUP 3 * 1 Department of Informatics, Széchenyi István University, Egyetem tér 1, 9026 Győr, Hungary 2 Department of Automation and Information Technology, Transilvania University of Brasov, 5 Mihai Viteazu Street, corp V, et. 3, 500174 Brasov, Romania cp@unitbv.ro 3 Department of Automation and Applied Informatics, University Politehnica of Timisoara, 2 V. Parvan Avenue, 300223 Timisoara, Romania radu.precup@upt.ro (*Corresponding author) Abstract: This paper proposes a cost-effective approach to the design of nonlinear state-space control systems. The approach is supported by a geometrical illustration of systems evolution in the state space, by the Lyapunov’s direct method, the native behaviour of the controlled process, and the desired system matrix. The method is exemplifed through the medium of a real- world process represented by the pendulum-cart system laboratory equipment. Keywords: State-space control systems, Nonlinear systems, Native behaviour, Lyapunov’s direct method. Studies in Informatics and Control, 27(1) 5-14, March 2018 https://doi.org/10.24846/v27i1y201801