This paper proposes a sliding mode investment policy design for nonlinear stochastic financial systems which can be represented by the well-known Takagi–Sugeno fuzzy model. When modeling the financial systems, it is more important to consider the unpredictable investment changes and worldwide unpredictable events which can be regarded as external disturbances. The equivalent-input-disturbance (EID) approach combined with sliding mode investment policy design is implemented to reject the unpredictable investment changes for having better investment. Moreover, the Luenberger state observer is constructed for the addressed financial system to estimate the unpredictable investment changes and worldwide unpredictable events. More precisely, a sliding mode investment policy design is developed by solving the obtained linear matrix inequality (LMI)-based constrained algorithm. Finally, the obtained results of the addressed fuzzy stochastic financial system are verified through numerical simulation to show efficiency of the proposed sliding mode investment policy design.

Introduction

In our day-to-day life, financial market is more important in which individuals exchange money related securities and commodities at low exchanges costs [1,2]. In order to stabilize the real economy of the companies, investors and governments, it is much essential to analyze the dynamical behavior between the financial market and the real economy. In general, the main objective of the companies, investors and governments are to increase the profit and reduce the risk. Recently, significant attention has been paid by the research communities on studies of financial systems due to complex process of business operations. In general, financial systems are influenced by a several economic factors, such as national and international situation changes, the variable interest rate, wrong economy policy, oil price change and unpredictable investment-environmental changes [3]. Moreover, in practice, many economic factors are not always be deterministic due to unpredictable sudden investments, wars and natural disorder. Therefore, in the dynamics of financial control systems these kind of unknown disturbance factors should be taken into consideration. On the other hand, the disturbance rejections in dynamical control systems can be handled by various design methodologies [4–۹]. In particular, the sliding mode control (SMC) is one of the most recognized controller to reject the effects of matched disturbances and the modeling error in the dynamical control system [10–۱۵]. Generally, sliding mode control contains two steps; one is to design the sliding surface in which the system has desired properties such as stability, disturbance rejection capability and tracking ability and the next is to design the discontinuous controller such that the system state reach the sliding surface in the finite time [16–۱۹].