Containment control problem can be categorized into static and dynamic leader scenarios while dynamic leader containment control problems are less developed. Based on the literature, most researches in dynamic leader containment control problems while considering bounded reference inputs and leaders’ states, have utilized protocols based on non-smooth functions. However, in addition to the limitation of bounded reference inputs and leaders’ states, utilizing non-smooth protocols can result problems such as chattering, large control signals and also undamped oscillations especially in the presence of time-delay. Therefore, in this dissertation in order to avoid the mentioned problems, it is assumed that the leaders’ reference inputs are polynomial-type signals with finite and known degree. Based on this, smooth proportional-integral type protocols with one or nested integrals are applied to provide the preliminaries to avoid the mentioned limitations and deficiencies of non-smooth protocols. Since time-delay in receiving/processing of the data has major influences on performance and stability of the multi-agent systems, in this dissertation time-delays are considered. First of all, the proportional-integral type protocol in multi-agent systems with certain integral-type dynamics and constant homogenous input time-delays are studied. Thereafter, utilizing the proportional-integral type protocol containment control problem in multi-agent systems with different dynamics such as canonical controllable type, general linear type and nonlinear type with Lipschitz nonlinearity in the presence of heterogonous matched uncertainties and considering homogenous constant and time-varying delays in input and communication, are investigated. In this dissertation, assuming the multi-agent system in the steady-state condition, switch in the communication graph is considered. Finally, considering all the mentioned assumptions and goals, appropriate Lyapunov-Krasovskii Functional are defined and utilizing them some Linear Matrix Inequalities (LMIs) are extracted. Solving these LMIs, suitable gains of the proportional-integral type protocol for achieving zero containment error with expected convergence rate, are attained. In this dissertation, some numerical simulations are given to verify the theoretical analysis. Keywords: Multi-agent systems, Containment control, Dynamic leaders, Uncertainty, Time-delay, Proportional-Integral controller